(4*cos(3*pi-b)-sin(3*pi/2 ... ))/(5*cos(b-pi))еслиb=1/2 (упростите выражение)

Вы ввели

                     /3*pi    \
4*cos(3*pi - b) - sin|---- + b|
                     \ 2      /
-------------------------------
         5*cos(b - pi)         

$$\frac{- \sin{\left(b + \frac{3 \pi}{2} \right)} + 4 \cos{\left(- b + 3 \pi \right)}}{5 \cos{\left(b - \pi \right)}}$$

Подстановка условия

(4*cos(3*pi - b) - sin((3*pi)/2 + b))/(5*cos(b - pi)) при b = 1/2

(4*cos(3*pi - b) - sin((3*pi)/2 + b))/(5*cos(b - pi))

$$\frac{1}{5 \cos{\left (b - \pi \right )}} \left(- \sin{\left (b + \frac{3 \pi}{2} \right )} + 4 \cos{\left (- b + 3 \pi \right )}\right)$$

(4*cos(3*pi - (1/2)) - sin((3*pi)/2 + (1/2)))/(5*cos((1/2) - pi))

$$\frac{1}{5 \cos{\left ((1/2) - \pi \right )}} \left(- \sin{\left ((1/2) + \frac{3 \pi}{2} \right )} + 4 \cos{\left (- (1/2) + 3 \pi \right )}\right)$$

(4*cos(3*pi - 1/2) - sin((3*pi)/2 + 1/2))/(5*cos(1/2 - pi))

$$\frac{1}{5 \cos{\left (- \pi + \frac{1}{2} \right )}} \left(4 \cos{\left (- \frac{1}{2} + 3 \pi \right )} - \sin{\left (\frac{1}{2} + \frac{3 \pi}{2} \right )}\right)$$

3/5

$$\frac{3}{5}$$

Степени

                                       /     /     3*pi\      /    3*pi\\
                                       |   I*|-b - ----|    I*|b + ----||
                                       |     \      2  /      \     2  /|
   I*(b - 3*pi)      I*(-b + 3*pi)   I*\- e              + e            /
2*e             + 2*e              + ------------------------------------
                                                      2                  
-------------------------------------------------------------------------
                         I*(pi - b)      I*(b - pi)                      
                      5*e             5*e                                
                      ------------- + -------------                      
                            2               2                            

$$\frac{\frac{i \left(- e^{i \left(- b - \frac{3 \pi}{2}\right)} + e^{i \left(b + \frac{3 \pi}{2}\right)}\right)}{2} + 2 e^{i \left(- b + 3 \pi\right)} + 2 e^{i \left(b - 3 \pi\right)}}{\frac{5 e^{i \left(\pi - b\right)}}{2} + \frac{5 e^{i \left(b - \pi\right)}}{2}}$$

3/5

$$\frac{3}{5}$$

cos(b)   4*cos(3*pi - b)
------ + ---------------
  5             5       
------------------------
      cos(b - pi)       

$$\frac{\frac{\cos{\left(b \right)}}{5} + \frac{4 \cos{\left(- b + 3 \pi \right)}}{5}}{\cos{\left(b - \pi \right)}}$$

Численный ответ

0.2*(-sin(3*pi/2 + b) + 4.0*cos(3*pi - b))/cos(b - pi)

Рациональный знаменатель

3/5

$$\frac{3}{5}$$

Объединение рациональных выражений

 /     /2*b + 3*pi\           \ 
-|- sin|----------| - 4*cos(b)| 
 \     \    2     /           / 
--------------------------------
            5*cos(b)            

$$- \frac{- \sin{\left(\frac{2 b + 3 \pi}{2} \right)} - 4 \cos{\left(b \right)}}{5 \cos{\left(b \right)}}$$

Общее упрощение

3/5

$$\frac{3}{5}$$

Собрать выражение

3/5

$$\frac{3}{5}$$

Общий знаменатель

  -3*cos(b)  
-------------
5*cos(b - pi)

$$- \frac{3 \cos{\left(b \right)}}{5 \cos{\left(b - \pi \right)}}$$

Тригонометрическая часть

/  //                                       /           /    pi\           \\     //                         1                            for And(im(b) = 0, (pi - b) mod 2*pi = 0)\\ //                         1                            for And(im(b) = 0, (pi + b) mod 2*pi = 0)\
|  ||              0                 for And|im(b) = 0, |b + --| mod pi = 0||     ||                                                                                               || ||                                                                                               |
|  ||                                       \           \    2 /           /|     || //     1        for And(im(b) = 0, b mod 2*pi = 0)\                                           || || //     1        for And(im(b) = 0, b mod 2*pi = 0)\                                           |
|  ||                                                                       |     || ||                                                |                                           || || ||                                                |                                           |
|  ||             -2                                                        |     || ||        2/b\                                    |                                           || || ||       2/b\                                     |                                           |
|- |<------------------------------                 otherwise               | + 4*|< ||-1 + cot |-|                                    |                                           ||*|< ||1 + cot |-|                                     |                                           |
|  ||/         1      \    /b   pi\                                         |     ||-|<         \2/                                    |                  otherwise                || ||-|<        \2/                                     |                  otherwise                |
|  |||1 + ------------|*cot|- + --|                                         |     || ||------------              otherwise             |                                           || || ||------------              otherwise             |                                           |
|  |||       2/b   pi\|    \2   4 /                                         |     || ||       2/b\                                     |                                           || || ||        2/b\                                    |                                           |
|  |||    cot |- + --||                                                     |     || ||1 + cot |-|                                     |                                           || || ||-1 + cot |-|                                    |                                           |
\  \\\        \2   4 //                                                     /     \\ \\        \2/                                     /                                           // \\ \\         \2/                                    /                                           /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                           5                                                                                                                                            

$$\frac{\left(\left(- \begin{cases} 0 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \frac{\pi}{2}\right) \bmod \pi = 0 \\- \frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{b}{2} + \frac{\pi}{4} \right)}}\right) \cot{\left(\frac{b}{2} + \frac{\pi}{4} \right)}} & \text{otherwise} \end{cases}\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(\pi - b\right) \bmod 2 \pi = 0 \\- \begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge b \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{b}{2} \right)} - 1}{\cot^{2}{\left(\frac{b}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right)\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \pi\right) \bmod 2 \pi = 0 \\- \begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge b \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{b}{2} \right)} + 1}{\cot^{2}{\left(\frac{b}{2} \right)} - 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)}{5}$$

                            /b   pi\
-4*cos(b) + (1 + sin(b))*cot|- + --|
                            \2   4 /
------------------------------------
        /       2/b\\    2/b\       
      5*|1 - cot |-||*sin |-|       
        \        \2//     \2/       

$$\frac{\left(\sin{\left(b \right)} + 1\right) \cot{\left(\frac{b}{2} + \frac{\pi}{4} \right)} - 4 \cos{\left(b \right)}}{5 \cdot \left(1 - \cot^{2}{\left(\frac{b}{2} \right)}\right) \sin^{2}{\left(\frac{b}{2} \right)}}$$

              /      /b   pi\       /       2/b\\\
              | 2*cot|- + --|     4*|1 - cot |-|||
/       2/b\\ |      \2   4 /       \        \2//|
|1 + cot |-||*|---------------- + ---------------|
\        \2// |       2/b   pi\            2/b\  |
              |1 + cot |- + --|     1 + cot |-|  |
              \        \2   4 /             \2/  /
--------------------------------------------------
                   /       2/b\\                  
                 5*|1 - cot |-||                  
                   \        \2//                  

$$\frac{\left(\frac{4 \cdot \left(1 - \cot^{2}{\left(\frac{b}{2} \right)}\right)}{\cot^{2}{\left(\frac{b}{2} \right)} + 1} + \frac{2 \cot{\left(\frac{b}{2} + \frac{\pi}{4} \right)}}{\cot^{2}{\left(\frac{b}{2} + \frac{\pi}{4} \right)} + 1}\right) \left(\cot^{2}{\left(\frac{b}{2} \right)} + 1\right)}{5 \cdot \left(1 - \cot^{2}{\left(\frac{b}{2} \right)}\right)}$$

 /               /    pi\\ 
-|-4*cos(b) + sin|b + --|| 
 \               \    2 // 
---------------------------
          5*cos(b)         

$$- \frac{\sin{\left(b + \frac{\pi}{2} \right)} - 4 \cos{\left(b \right)}}{5 \cos{\left(b \right)}}$$

       /    pi\   (1 + sin(b))*cos(b)
- 4*sin|b + --| + -------------------
       \    2 /           2/b   pi\  
                     2*sin |- + --|  
                           \2   4 /  
-------------------------------------
        /        2    \              
        |     sin (b) |    2/b\      
      5*|1 - ---------|*sin |-|      
        |         4/b\|     \2/      
        |    4*sin |-||              
        \          \2//              

$$\frac{\frac{\left(\sin{\left(b \right)} + 1\right) \cos{\left(b \right)}}{2 \sin^{2}{\left(\frac{b}{2} + \frac{\pi}{4} \right)}} - 4 \sin{\left(b + \frac{\pi}{2} \right)}}{5 \cdot \left(1 - \frac{\sin^{2}{\left(b \right)}}{4 \sin^{4}{\left(\frac{b}{2} \right)}}\right) \sin^{2}{\left(\frac{b}{2} \right)}}$$

/      1   \ /             1 + sin(b)\
|1 - ------|*|-4*cos(b) + -----------|
\    cos(b)/ |               /b   pi\|
             |            tan|- + --||
             \               \2   4 //
--------------------------------------
                4/b\    2/b\          
          40*cos |-|*tan |-|          
                 \4/     \4/          

$$\frac{\left(1 - \frac{1}{\cos{\left(b \right)}}\right) \left(\frac{\sin{\left(b \right)} + 1}{\tan{\left(\frac{b}{2} + \frac{\pi}{4} \right)}} - 4 \cos{\left(b \right)}\right)}{40 \cos^{4}{\left(\frac{b}{4} \right)} \tan^{2}{\left(\frac{b}{4} \right)}}$$

/  //                                    /           /    pi\           \\                                                               \                                                          
|  ||             0               for And|im(b) = 0, |b + --| mod pi = 0||                                                               |                                                          
|  ||                                    \           \    2 /           /|                                                               |                                                          
|  ||                                                                    |                                                               |                                                          
|  ||            2/b   pi\                                               |                                                               | //     1       for And(im(b) = 0, (pi + b) mod 2*pi = 0)\
|  ||      -4*sin |- + --|                                               |     //     1        for And(im(b) = 0, (pi - b) mod 2*pi = 0)\| ||                                                      |
|  ||             \2   4 /                                               |     ||                                                       || ||    -1                                                |
|- |<---------------------------                 otherwise               | + 4*|<    /    pi\                                           ||*|<-----------                  otherwise                |
|  ||/         4/b   pi\\                                                |     ||-sin|b + --|                  otherwise                || ||   /    pi\                                           |
|  |||    4*sin |- + --||                                                |     \\    \    2 /                                           /| ||sin|b + --|                                           |
|  |||          \2   4 /|                                                |                                                               | \\   \    2 /                                           /
|  |||1 + --------------|*cos(b)                                         |                                                               |                                                          
|  |||          2       |                                                |                                                               |                                                          
|  ||\       cos (b)    /                                                |                                                               |                                                          
\  \\                                                                    /                                                               /                                                          
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                 5                                                                                                  

$$\frac{\left(\left(- \begin{cases} 0 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \frac{\pi}{2}\right) \bmod \pi = 0 \\- \frac{4 \sin^{2}{\left(\frac{b}{2} + \frac{\pi}{4} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{b}{2} + \frac{\pi}{4} \right)}}{\cos^{2}{\left(b \right)}} + 1\right) \cos{\left(b \right)}} & \text{otherwise} \end{cases}\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(\pi - b\right) \bmod 2 \pi = 0 \\- \sin{\left(b + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)\right)\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \pi\right) \bmod 2 \pi = 0 \\- \frac{1}{\sin{\left(b + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)}{5}$$

/                                                                                 //     1        for And(im(b) = 0, (pi - b) mod 2*pi = 0)\\ //     1        for And(im(b) = 0, (pi + b) mod 2*pi = 0)\
|  //                                       /           /    pi\           \\     ||                                                       || ||                                                       |
|  ||              0                 for And|im(b) = 0, |b + --| mod pi = 0||     ||        1                                              || ||       1                                               |
|  ||                                       \           \    2 /           /|     ||-1 + -------                                           || ||1 + -------                                            |
|  ||                                                                       |     ||        2/b\                                           || ||       2/b\                                            |
|  ||             -2                                                        |     ||     cot |-|                                           || ||    cot |-|                                            |
|- |<------------------------------                 otherwise               | + 4*|<         \2/                                           ||*|<        \2/                                            |
|  ||/         1      \    /b   pi\                                         |     ||------------                  otherwise                || ||------------                  otherwise                |
|  |||1 + ------------|*cot|- + --|                                         |     ||       1                                               || ||        1                                              |
|  |||       2/b   pi\|    \2   4 /                                         |     ||1 + -------                                            || ||-1 + -------                                           |
|  |||    cot |- + --||                                                     |     ||       2/b\                                            || ||        2/b\                                           |
|  \\\        \2   4 //                                                     /     ||    cot |-|                                            || ||     cot |-|                                           |
\                                                                                 \\        \2/                                            // \\         \2/                                           /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                   5                                                                                                    

$$\frac{\left(\left(- \begin{cases} 0 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \frac{\pi}{2}\right) \bmod \pi = 0 \\- \frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{b}{2} + \frac{\pi}{4} \right)}}\right) \cot{\left(\frac{b}{2} + \frac{\pi}{4} \right)}} & \text{otherwise} \end{cases}\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(\pi - b\right) \bmod 2 \pi = 0 \\\frac{-1 + \frac{1}{\cot^{2}{\left(\frac{b}{2} \right)}}}{1 + \frac{1}{\cot^{2}{\left(\frac{b}{2} \right)}}} & \text{otherwise} \end{cases}\right)\right)\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \pi\right) \bmod 2 \pi = 0 \\\frac{1 + \frac{1}{\cot^{2}{\left(\frac{b}{2} \right)}}}{-1 + \frac{1}{\cot^{2}{\left(\frac{b}{2} \right)}}} & \text{otherwise} \end{cases}\right)}{5}$$

 /       1          4   \        
-|- ----------- - ------|*sec(b) 
 \  sec(pi + b)   sec(b)/        
---------------------------------
                5                

$$- \frac{\left(- \frac{1}{\sec{\left(b + \pi \right)}} - \frac{4}{\sec{\left(b \right)}}\right) \sec{\left(b \right)}}{5}$$

          -6*cos(b)           
------------------------------
               /        2    \
               |     sin (b) |
5*(1 - cos(b))*|1 - ---------|
               |         4/b\|
               |    4*sin |-||
               \          \2//

$$- \frac{6 \cos{\left(b \right)}}{5 \cdot \left(1 - \frac{\sin^{2}{\left(b \right)}}{4 \sin^{4}{\left(\frac{b}{2} \right)}}\right) \left(1 - \cos{\left(b \right)}\right)}$$

                     /            /       /b\\             \
                     |            |1 - tan|-||*(1 + sin(b))|
   2/b\ /      1   \ |            \       \2//             |
csc |-|*|1 - ------|*|-4*cos(b) + -------------------------|
    \2/ \    cos(b)/ |                           /b\       |
                     |                    1 + tan|-|       |
                     \                           \2/       /
------------------------------------------------------------
                             10                             

$$\frac{\left(1 - \frac{1}{\cos{\left(b \right)}}\right) \left(\frac{\left(1 - \tan{\left(\frac{b}{2} \right)}\right) \left(\sin{\left(b \right)} + 1\right)}{\tan{\left(\frac{b}{2} \right)} + 1} - 4 \cos{\left(b \right)}\right) \csc^{2}{\left(\frac{b}{2} \right)}}{10}$$

/  //                         /           /    pi\           \\                                                                  \                                                              
|  ||       0          for And|im(b) = 0, |b + --| mod pi = 0||     //       1         for And(im(b) = 0, (pi - b) mod 2*pi = 0)\| //       1         for And(im(b) = 0, (pi + b) mod 2*pi = 0)\
|  ||                         \           \    2 /           /|     ||                                                          || ||                                                          |
|  ||                                                         |     || /       2/b\\                                            || || /       2/b\\                                            |
|  ||       /b   pi\                                          |     ||-|1 - tan |-||                                            || ||-|1 + tan |-||                                            |
|- |< -2*tan|- + --|                                          | + 4*|< \        \2//                                            ||*|< \        \2//                                            |
|  ||       \2   4 /                                          |     ||---------------                  otherwise                || ||---------------                  otherwise                |
|  ||----------------                 otherwise               |     ||         2/b\                                             || ||         2/b\                                             |
|  ||       2/b   pi\                                         |     ||  1 + tan |-|                                             || ||  1 - tan |-|                                             |
|  ||1 + tan |- + --|                                         |     \\          \2/                                             /| \\          \2/                                             /
\  \\        \2   4 /                                         /                                                                  /                                                              
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                               5                                                                                                

$$\frac{\left(\left(- \begin{cases} 0 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \frac{\pi}{2}\right) \bmod \pi = 0 \\- \frac{2 \tan{\left(\frac{b}{2} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{b}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(\pi - b\right) \bmod 2 \pi = 0 \\- \frac{1 - \tan^{2}{\left(\frac{b}{2} \right)}}{\tan^{2}{\left(\frac{b}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)\right)\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \pi\right) \bmod 2 \pi = 0 \\- \frac{\tan^{2}{\left(\frac{b}{2} \right)} + 1}{1 - \tan^{2}{\left(\frac{b}{2} \right)}} & \text{otherwise} \end{cases}\right)}{5}$$

/  //                         /           /    pi\           \\                                                               \                                                           
|  ||       0          for And|im(b) = 0, |b + --| mod pi = 0||     //     1        for And(im(b) = 0, (pi - b) mod 2*pi = 0)\| //     1        for And(im(b) = 0, (pi + b) mod 2*pi = 0)\
|  ||                         \           \    2 /           /|     ||                                                       || ||                                                       |
|  ||                                                         |     ||        2/b\                                           || ||       2/b\                                            |
|  ||       /b   pi\                                          |     ||-1 + tan |-|                                           || ||1 + tan |-|                                            |
|- |< -2*tan|- + --|                                          | + 4*|<         \2/                                           ||*|<        \2/                                            |
|  ||       \2   4 /                                          |     ||------------                  otherwise                || ||------------                  otherwise                |
|  ||----------------                 otherwise               |     ||       2/b\                                            || ||        2/b\                                           |
|  ||       2/b   pi\                                         |     ||1 + tan |-|                                            || ||-1 + tan |-|                                           |
|  ||1 + tan |- + --|                                         |     \\        \2/                                            /| \\         \2/                                           /
\  \\        \2   4 /                                         /                                                               /                                                           
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                            5                                                                                             

$$\frac{\left(\left(- \begin{cases} 0 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \frac{\pi}{2}\right) \bmod \pi = 0 \\- \frac{2 \tan{\left(\frac{b}{2} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{b}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(\pi - b\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(\frac{b}{2} \right)} - 1}{\tan^{2}{\left(\frac{b}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)\right)\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \pi\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(\frac{b}{2} \right)} + 1}{\tan^{2}{\left(\frac{b}{2} \right)} - 1} & \text{otherwise} \end{cases}\right)}{5}$$

 /  1           4     \    /pi    \ 
-|------ - -----------|*csc|-- - b| 
 |sec(b)      /pi    \|    \2     / 
 |         csc|-- - b||             
 \            \2     //             
------------------------------------
                 5                  

$$- \frac{\left(\frac{1}{\sec{\left(b \right)}} - \frac{4}{\csc{\left(- b + \frac{\pi}{2} \right)}}\right) \csc{\left(- b + \frac{\pi}{2} \right)}}{5}$$

     /     7*pi\         
4*sin|-b + ----| + cos(b)
     \      2  /         
-------------------------
           /    pi\      
      5*sin|b - --|      
           \    2 /      

$$\frac{4 \sin{\left(- b + \frac{7 \pi}{2} \right)} + \cos{\left(b \right)}}{5 \sin{\left(b - \frac{\pi}{2} \right)}}$$

               /           /b\                   \
               |      2*tan|-|                   |
               |           \2/                   |
               |1 + -----------                  |
               |           2/b\     /       2/b\\|
             2 |    1 + tan |-|   4*|1 - tan |-|||
/       2/b\\  |            \2/     \        \2//|
|1 + tan |-|| *|--------------- - ---------------|
\        \4//  |     /b   pi\              2/b\  |
               |  tan|- + --|       1 + tan |-|  |
               \     \2   4 /               \2/  /
--------------------------------------------------
                /       1   \    2/b\             
             20*|1 - -------|*tan |-|             
                |       2/b\|     \4/             
                |    tan |-||                     
                \        \2//                     

$$\frac{\left(\frac{1 + \frac{2 \tan{\left(\frac{b}{2} \right)}}{\tan^{2}{\left(\frac{b}{2} \right)} + 1}}{\tan{\left(\frac{b}{2} + \frac{\pi}{4} \right)}} - \frac{4 \cdot \left(1 - \tan^{2}{\left(\frac{b}{2} \right)}\right)}{\tan^{2}{\left(\frac{b}{2} \right)} + 1}\right) \left(\tan^{2}{\left(\frac{b}{4} \right)} + 1\right)^{2}}{20 \cdot \left(1 - \frac{1}{\tan^{2}{\left(\frac{b}{2} \right)}}\right) \tan^{2}{\left(\frac{b}{4} \right)}}$$

        /                /      1   \    /b   pi\\
        |                |1 + ------|*csc|- + --||
   2/b\ |       4        \    csc(b)/    \2   4 /|
csc |-|*|- ----------- + ------------------------|
    \2/ |     /pi    \           /  b   pi\      |
        |  csc|-- - b|        csc|- - + --|      |
        \     \2     /           \  2   4 /      /
--------------------------------------------------
                 /         2/b\   \               
                 |      csc |-|   |               
                 |          \2/   |               
               5*|1 - ------------|               
                 |       2/pi   b\|               
                 |    csc |-- - -||               
                 \        \2    2//               

$$\frac{\left(\frac{\left(1 + \frac{1}{\csc{\left(b \right)}}\right) \csc{\left(\frac{b}{2} + \frac{\pi}{4} \right)}}{\csc{\left(- \frac{b}{2} + \frac{\pi}{4} \right)}} - \frac{4}{\csc{\left(- b + \frac{\pi}{2} \right)}}\right) \csc^{2}{\left(\frac{b}{2} \right)}}{5 \left(- \frac{\csc^{2}{\left(\frac{b}{2} \right)}}{\csc^{2}{\left(- \frac{b}{2} + \frac{\pi}{2} \right)}} + 1\right)}$$

/  //                         /           /    pi\           \\                                                          \                                                     
|  ||       0          for And|im(b) = 0, |b + --| mod pi = 0||                                                          |                                                     
|  ||                         \           \    2 /           /|                                                          |                                                     
|  ||                                                         |                                                          | //  1     for And(im(b) = 0, (pi + b) mod 2*pi = 0)\
|  ||       /b   pi\                                          |     //   1     for And(im(b) = 0, (pi - b) mod 2*pi = 0)\| ||                                                 |
|- |< -2*tan|- + --|                                          | + 4*|<                                                  ||*|< -1                                              |
|  ||       \2   4 /                                          |     \\-cos(b)                  otherwise                /| ||------                  otherwise                |
|  ||----------------                 otherwise               |                                                          | \\cos(b)                                           /
|  ||       2/b   pi\                                         |                                                          |                                                     
|  ||1 + tan |- + --|                                         |                                                          |                                                     
\  \\        \2   4 /                                         /                                                          /                                                     
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                       5                                                                                       

$$\frac{\left(\left(- \begin{cases} 0 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \frac{\pi}{2}\right) \bmod \pi = 0 \\- \frac{2 \tan{\left(\frac{b}{2} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{b}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(\pi - b\right) \bmod 2 \pi = 0 \\- \cos{\left(b \right)} & \text{otherwise} \end{cases}\right)\right)\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \pi\right) \bmod 2 \pi = 0 \\- \frac{1}{\cos{\left(b \right)}} & \text{otherwise} \end{cases}\right)}{5}$$

                                                                                                                    //                   /           b           \\
                                                                                                                    ||   zoo      for And|im(b) = 0, - mod pi = 0||
/    //  1     for And(im(b) = 0, b mod 2*pi = 0)\   /    //  0     for And(im(b) = 0, b mod pi = 0)\\    /b   pi\\ ||                   \           2           /|
|- 4*|<                                          | + |1 + |<                                        ||*cot|- + --||*|<                                            |
\    \\cos(b)              otherwise             /   \    \\sin(b)             otherwise            //    \2   4 // ||    2                                       |
                                                                                                                    ||----------             otherwise            |
                                                                                                                    \\1 - cos(b)                                  /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                            /       2/b\\                                                                          
                                                                          5*|1 - cot |-||                                                                          
                                                                            \        \2//                                                                          

$$\frac{\left(\left(\left(\left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge b \bmod \pi = 0 \\\sin{\left(b \right)} & \text{otherwise} \end{cases}\right) + 1\right) \cot{\left(\frac{b}{2} + \frac{\pi}{4} \right)}\right) - \left(4 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge b \bmod 2 \pi = 0 \\\cos{\left(b \right)} & \text{otherwise} \end{cases}\right)\right)\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \frac{b}{2} \bmod \pi = 0 \\\frac{2}{1 - \cos{\left(b \right)}} & \text{otherwise} \end{cases}\right)}{5 \cdot \left(1 - \cot^{2}{\left(\frac{b}{2} \right)}\right)}$$

/  //                                    /           /    pi\           \\                                                          \                                                     
|  ||             0               for And|im(b) = 0, |b + --| mod pi = 0||                                                          |                                                     
|  ||                                    \           \    2 /           /|                                                          |                                                     
|  ||                                                                    |                                                          | //  1     for And(im(b) = 0, (pi + b) mod 2*pi = 0)\
|  ||              /       /b\\                                          |     //   1     for And(im(b) = 0, (pi - b) mod 2*pi = 0)\| ||                                                 |
|- |<-(1 - sin(b))*|1 + tan|-||                                          | + 4*|<                                                  ||*|< -1                                              |
|  ||              \       \2//                                          |     \\-cos(b)                  otherwise                /| ||------                  otherwise                |
|  ||---------------------------                 otherwise               |                                                          | \\cos(b)                                           /
|  ||                /b\                                                 |                                                          |                                                     
|  ||         1 - tan|-|                                                 |                                                          |                                                     
\  \\                \2/                                                 /                                                          /                                                     
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                            5                                                                                             

$$\frac{\left(\left(- \begin{cases} 0 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \frac{\pi}{2}\right) \bmod \pi = 0 \\- \frac{\left(1 - \sin{\left(b \right)}\right) \left(\tan{\left(\frac{b}{2} \right)} + 1\right)}{1 - \tan{\left(\frac{b}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(\pi - b\right) \bmod 2 \pi = 0 \\- \cos{\left(b \right)} & \text{otherwise} \end{cases}\right)\right)\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \pi\right) \bmod 2 \pi = 0 \\- \frac{1}{\cos{\left(b \right)}} & \text{otherwise} \end{cases}\right)}{5}$$

/  //                                       /           /    pi\           \\                                                          \                                                     
|  ||              0                 for And|im(b) = 0, |b + --| mod pi = 0||                                                          |                                                     
|  ||                                       \           \    2 /           /|                                                          |                                                     
|  ||                                                                       |                                                          |                                                     
|  ||              /b   pi\                                                 |                                                          |                                                     
|  ||        -2*cos|- - --|                                                 |                                                          | //  1     for And(im(b) = 0, (pi + b) mod 2*pi = 0)\
|  ||              \2   4 /                                                 |     //   1     for And(im(b) = 0, (pi - b) mod 2*pi = 0)\| ||                                                 |
|- |<------------------------------                 otherwise               | + 4*|<                                                  ||*|< -1                                              |
|  ||/       2/b   pi\\                                                     |     \\-cos(b)                  otherwise                /| ||------                  otherwise                |
|  |||    cos |- - --||                                                     |                                                          | \\cos(b)                                           /
|  |||        \2   4 /|    /b   pi\                                         |                                                          |                                                     
|  |||1 + ------------|*cos|- + --|                                         |                                                          |                                                     
|  |||       2/b   pi\|    \2   4 /                                         |                                                          |                                                     
|  |||    cos |- + --||                                                     |                                                          |                                                     
\  \\\        \2   4 //                                                     /                                                          /                                                     
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                              5                                                                                              

$$\frac{\left(\left(- \begin{cases} 0 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \frac{\pi}{2}\right) \bmod \pi = 0 \\- \frac{2 \cos{\left(\frac{b}{2} - \frac{\pi}{4} \right)}}{\left(\frac{\cos^{2}{\left(\frac{b}{2} - \frac{\pi}{4} \right)}}{\cos^{2}{\left(\frac{b}{2} + \frac{\pi}{4} \right)}} + 1\right) \cos{\left(\frac{b}{2} + \frac{\pi}{4} \right)}} & \text{otherwise} \end{cases}\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(\pi - b\right) \bmod 2 \pi = 0 \\- \cos{\left(b \right)} & \text{otherwise} \end{cases}\right)\right)\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \pi\right) \bmod 2 \pi = 0 \\- \frac{1}{\cos{\left(b \right)}} & \text{otherwise} \end{cases}\right)}{5}$$

                                                                                                                               //                       /           b           \\
                                                                                                                               ||     zoo        for And|im(b) = 0, - mod pi = 0||
/    //     1        for And(im(b) = 0, b mod 2*pi = 0)\   /    //     0       for And(im(b) = 0, b mod pi = 0)\\            \ ||                       \           2           /|
|    ||                                                |   |    ||                                             ||            | ||                                                |
|    ||        2/b\                                    |   |    ||       /b\                                   ||            | ||             2                                  |
|    ||-1 + cot |-|                                    |   |    ||  2*cot|-|                                   ||    /b   pi\| ||/       2/b\\                                   |
|- 4*|<         \2/                                    | + |1 + |<       \2/                                   ||*cot|- + --||*|<|1 + cot |-||                                   |
|    ||------------              otherwise             |   |    ||-----------             otherwise            ||    \2   4 /| ||\        \4//                                   |
|    ||       2/b\                                     |   |    ||       2/b\                                  ||            | ||--------------             otherwise            |
|    ||1 + cot |-|                                     |   |    ||1 + cot |-|                                  ||            | ||       2/b\                                     |
\    \\        \2/                                     /   \    \\        \2/                                  //            / ||  4*cot |-|                                     |
                                                                                                                               ||        \4/                                     |
                                                                                                                               \\                                                /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                   /       2/b\\                                                                                  
                                                                                 5*|1 - cot |-||                                                                                  
                                                                                   \        \2//                                                                                  

$$\frac{\left(\left(\left(\left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge b \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{b}{2} \right)}}{\cot^{2}{\left(\frac{b}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) + 1\right) \cot{\left(\frac{b}{2} + \frac{\pi}{4} \right)}\right) - \left(4 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge b \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{b}{2} \right)} - 1}{\cot^{2}{\left(\frac{b}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)\right)\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \frac{b}{2} \bmod \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{b}{4} \right)} + 1\right)^{2}}{4 \cot^{2}{\left(\frac{b}{4} \right)}} & \text{otherwise} \end{cases}\right)}{5 \cdot \left(1 - \cot^{2}{\left(\frac{b}{2} \right)}\right)}$$

/  //                                         /           /    pi\           \\                                                              \                                                           
|  ||               0                  for And|im(b) = 0, |b + --| mod pi = 0||                                                              |                                                           
|  ||                                         \           \    2 /           /|                                                              |                                                           
|  ||                                                                         |                                                              |                                                           
|  ||              /  b   pi\                                                 |     //     1       for And(im(b) = 0, (pi - b) mod 2*pi = 0)\|                                                           
|  ||        -2*csc|- - + --|                                                 |     ||                                                      || //     1        for And(im(b) = 0, (pi + b) mod 2*pi = 0)\
|  ||              \  2   4 /                                                 |     ||    -1                                                || ||                                                       |
|- |<--------------------------------                 otherwise               | + 4*|<-----------                  otherwise                ||*|<    /pi    \                                           |
|  ||/       2/  b   pi\\                                                     |     ||   /pi    \                                           || ||-csc|-- - b|                  otherwise                |
|  |||    csc |- - + --||                                                     |     ||csc|-- - b|                                           || \\    \2     /                                           /
|  |||        \  2   4 /|    /b   pi\                                         |     \\   \2     /                                           /|                                                           
|  |||1 + --------------|*csc|- + --|                                         |                                                              |                                                           
|  |||        2/b   pi\ |    \2   4 /                                         |                                                              |                                                           
|  |||     csc |- + --| |                                                     |                                                              |                                                           
\  \\\         \2   4 / /                                                     /                                                              /                                                           
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                    5                                                                                                    

$$\frac{\left(\left(- \begin{cases} 0 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \frac{\pi}{2}\right) \bmod \pi = 0 \\- \frac{2 \csc{\left(- \frac{b}{2} + \frac{\pi}{4} \right)}}{\left(\frac{\csc^{2}{\left(- \frac{b}{2} + \frac{\pi}{4} \right)}}{\csc^{2}{\left(\frac{b}{2} + \frac{\pi}{4} \right)}} + 1\right) \csc{\left(\frac{b}{2} + \frac{\pi}{4} \right)}} & \text{otherwise} \end{cases}\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(\pi - b\right) \bmod 2 \pi = 0 \\- \frac{1}{\csc{\left(- b + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right)\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \pi\right) \bmod 2 \pi = 0 \\- \csc{\left(- b + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)}{5}$$

             /           /         1     \    /b   pi\\
             |           |1 + -----------|*sec|- - --||
             |           |       /    pi\|    \2   4 /|
             |           |    sec|b - --||            |
   2/b   pi\ |    4      \       \    2 //            |
sec |- - --|*|- ------ + -----------------------------|
    \2   2 / |  sec(b)               /b   pi\         |
             |                    sec|- + --|         |
             \                       \2   4 /         /
-------------------------------------------------------
                    /       2/b   pi\\                 
                    |    sec |- - --||                 
                    |        \2   2 /|                 
                  5*|1 - ------------|                 
                    |         2/b\   |                 
                    |      sec |-|   |                 
                    \          \2/   /                 

$$\frac{\left(\frac{\left(1 + \frac{1}{\sec{\left(b - \frac{\pi}{2} \right)}}\right) \sec{\left(\frac{b}{2} - \frac{\pi}{4} \right)}}{\sec{\left(\frac{b}{2} + \frac{\pi}{4} \right)}} - \frac{4}{\sec{\left(b \right)}}\right) \sec^{2}{\left(\frac{b}{2} - \frac{\pi}{2} \right)}}{5 \cdot \left(1 - \frac{\sec^{2}{\left(\frac{b}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{b}{2} \right)}}\right)}$$

                 /            /       /b\\             \
                 |            |1 - tan|-||*(1 + sin(b))|
  /1      1    \ |            \       \2//             |
2*|- - --------|*|-4*cos(b) + -------------------------|
  \2   2*cos(b)/ |                           /b\       |
                 |                    1 + tan|-|       |
                 \                           \2/       /
--------------------------------------------------------
                     5*(1 - cos(b))                     

$$\frac{2 \cdot \left(\frac{1}{2} - \frac{1}{2 \cos{\left(b \right)}}\right) \left(\frac{\left(1 - \tan{\left(\frac{b}{2} \right)}\right) \left(\sin{\left(b \right)} + 1\right)}{\tan{\left(\frac{b}{2} \right)} + 1} - 4 \cos{\left(b \right)}\right)}{5 \cdot \left(1 - \cos{\left(b \right)}\right)}$$

/  //                                    /           /    pi\           \\                                                          \                                                      
|  ||             0               for And|im(b) = 0, |b + --| mod pi = 0||                                                          |                                                      
|  ||                                    \           \    2 /           /|                                                          |                                                      
|  ||                                                                    |                                                          |                                                      
|  ||              /       /b\\                                          |     //   1     for And(im(b) = 0, (pi - b) mod 2*pi = 0)\| //   1     for And(im(b) = 0, (pi + b) mod 2*pi = 0)\
|- |<-(1 - sin(b))*|1 + tan|-||                                          | + 4*|<                                                  ||*|<                                                  |
|  ||              \       \2//                                          |     \\-cos(b)                  otherwise                /| \\-sec(b)                  otherwise                /
|  ||---------------------------                 otherwise               |                                                          |                                                      
|  ||                /b\                                                 |                                                          |                                                      
|  ||         1 - tan|-|                                                 |                                                          |                                                      
\  \\                \2/                                                 /                                                          /                                                      
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                             5                                                                                             

$$\frac{\left(\left(- \begin{cases} 0 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \frac{\pi}{2}\right) \bmod \pi = 0 \\- \frac{\left(1 - \sin{\left(b \right)}\right) \left(\tan{\left(\frac{b}{2} \right)} + 1\right)}{1 - \tan{\left(\frac{b}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(\pi - b\right) \bmod 2 \pi = 0 \\- \cos{\left(b \right)} & \text{otherwise} \end{cases}\right)\right)\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \pi\right) \bmod 2 \pi = 0 \\- \sec{\left(b \right)} & \text{otherwise} \end{cases}\right)}{5}$$

/  //                /           /    pi\           \\                                                          \ //  1     for And(im(b) = 0, (pi + b) mod 2*pi = 0)\
|  ||   0     for And|im(b) = 0, |b + --| mod pi = 0||     //   1     for And(im(b) = 0, (pi - b) mod 2*pi = 0)\| ||                                                 |
|- |<                \           \    2 /           /| + 4*|<                                                  ||*|< -1                                              |
|  ||                                                |     \\-cos(b)                  otherwise                /| ||------                  otherwise                |
\  \\-cos(b)                 otherwise               /                                                          / \\cos(b)                                           /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                  5                                                                                   

$$\frac{\left(\left(- \begin{cases} 0 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \frac{\pi}{2}\right) \bmod \pi = 0 \\- \cos{\left(b \right)} & \text{otherwise} \end{cases}\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(\pi - b\right) \bmod 2 \pi = 0 \\- \cos{\left(b \right)} & \text{otherwise} \end{cases}\right)\right)\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \pi\right) \bmod 2 \pi = 0 \\- \frac{1}{\cos{\left(b \right)}} & \text{otherwise} \end{cases}\right)}{5}$$

/  //                         /           /    pi\           \\                                                                                                 \                                                                                             
|  ||       0          for And|im(b) = 0, |b + --| mod pi = 0||                                                                                                 |                                                                                             
|  ||                         \           \    2 /           /|                                                                                                 | //                      1                         for And(im(b) = 0, (pi + b) mod 2*pi = 0)\
|  ||                                                         |     //                      1                         for And(im(b) = 0, (pi - b) mod 2*pi = 0)\| ||                                                                                         |
|  ||       /b   pi\                                          |     ||                                                                                         || || //  1     for And(im(b) = 0, b mod 2*pi = 0)\                                           |
|- |< -2*tan|- + --|                                          | + 4*|< //  1     for And(im(b) = 0, b mod 2*pi = 0)\                                           ||*|< ||                                          |                                           |
|  ||       \2   4 /                                          |     ||-|<                                          |                  otherwise                || ||-|<  1                                       |                  otherwise                |
|  ||----------------                 otherwise               |     \\ \\cos(b)              otherwise             /                                           /| || ||------              otherwise             |                                           |
|  ||       2/b   pi\                                         |                                                                                                 | \\ \\cos(b)                                    /                                           /
|  ||1 + tan |- + --|                                         |                                                                                                 |                                                                                             
\  \\        \2   4 /                                         /                                                                                                 /                                                                                             
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                              5                                                                                                                               

$$\frac{\left(\left(- \begin{cases} 0 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \frac{\pi}{2}\right) \bmod \pi = 0 \\- \frac{2 \tan{\left(\frac{b}{2} + \frac{\pi}{4} \right)}}{\tan^{2}{\left(\frac{b}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(\pi - b\right) \bmod 2 \pi = 0 \\- \begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge b \bmod 2 \pi = 0 \\\cos{\left(b \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right)\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \pi\right) \bmod 2 \pi = 0 \\- \begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge b \bmod 2 \pi = 0 \\\frac{1}{\cos{\left(b \right)}} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)}{5}$$

 /     1          4   \        
-|----------- - ------|*sec(b) 
 |   /pi    \   sec(b)|        
 |csc|-- - b|         |        
 \   \2     /         /        
-------------------------------
               5               

$$- \frac{\left(- \frac{4}{\sec{\left(b \right)}} + \frac{1}{\csc{\left(- b + \frac{\pi}{2} \right)}}\right) \sec{\left(b \right)}}{5}$$

              /                                   /       1   \\
              |                                 4*|1 - -------||
              |                                   |       2/b\||
              |                                   |    tan |-|||
/       1   \ |              2                    \        \2//|
|1 + -------|*|------------------------------ + ---------------|
|       2/b\| |/         1      \    /b   pi\            1     |
|    tan |-|| ||1 + ------------|*tan|- + --|     1 + -------  |
\        \2// ||       2/b   pi\|    \2   4 /            2/b\  |
              ||    tan |- + --||                     tan |-|  |
              \\        \2   4 //                         \2/  /
----------------------------------------------------------------
                          /       1   \                         
                        5*|1 - -------|                         
                          |       2/b\|                         
                          |    tan |-||                         
                          \        \2//                         

$$\frac{\left(1 + \frac{1}{\tan^{2}{\left(\frac{b}{2} \right)}}\right) \left(\frac{4 \cdot \left(1 - \frac{1}{\tan^{2}{\left(\frac{b}{2} \right)}}\right)}{1 + \frac{1}{\tan^{2}{\left(\frac{b}{2} \right)}}} + \frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{b}{2} + \frac{\pi}{4} \right)}}\right) \tan{\left(\frac{b}{2} + \frac{\pi}{4} \right)}}\right)}{5 \cdot \left(1 - \frac{1}{\tan^{2}{\left(\frac{b}{2} \right)}}\right)}$$

            /       /    pi\\    /b   pi\
            |1 + cos|b - --||*cos|- + --|
            \       \    2 //    \2   4 /
-4*cos(b) + -----------------------------
                        /b   pi\         
                     cos|- - --|         
                        \2   4 /         
-----------------------------------------
      /         2/b\   \                 
      |      cos |-|   |                 
      |          \2/   |    2/b   pi\    
    5*|1 - ------------|*cos |- - --|    
      |       2/b   pi\|     \2   2 /    
      |    cos |- - --||                 
      \        \2   2 //                 

$$\frac{\frac{\left(\cos{\left(b - \frac{\pi}{2} \right)} + 1\right) \cos{\left(\frac{b}{2} + \frac{\pi}{4} \right)}}{\cos{\left(\frac{b}{2} - \frac{\pi}{4} \right)}} - 4 \cos{\left(b \right)}}{5 \left(- \frac{\cos^{2}{\left(\frac{b}{2} \right)}}{\cos^{2}{\left(\frac{b}{2} - \frac{\pi}{2} \right)}} + 1\right) \cos^{2}{\left(\frac{b}{2} - \frac{\pi}{2} \right)}}$$

-(-cos(pi + b) - 4*cos(b)) 
---------------------------
          5*cos(b)         

$$- \frac{- 4 \cos{\left(b \right)} - \cos{\left(b + \pi \right)}}{5 \cos{\left(b \right)}}$$

/  //                                       /           /    pi\           \\                                                         \                                                      
|  ||              0                 for And|im(b) = 0, |b + --| mod pi = 0||                                                         |                                                      
|  ||                                       \           \    2 /           /|                                                         |                                                      
|  ||                                                                       |                                                         |                                                      
|  ||              /b   pi\                                                 |                                                         |                                                      
|  ||        -2*sec|- + --|                                                 |     //  1     for And(im(b) = 0, (pi - b) mod 2*pi = 0)\|                                                      
|  ||              \2   4 /                                                 |     ||                                                 || //   1     for And(im(b) = 0, (pi + b) mod 2*pi = 0)\
|- |<------------------------------                 otherwise               | + 4*|< -1                                              ||*|<                                                  |
|  ||/       2/b   pi\\                                                     |     ||------                  otherwise                || \\-sec(b)                  otherwise                /
|  |||    sec |- + --||                                                     |     \\sec(b)                                           /|                                                      
|  |||        \2   4 /|    /b   pi\                                         |                                                         |                                                      
|  |||1 + ------------|*sec|- - --|                                         |                                                         |                                                      
|  |||       2/b   pi\|    \2   4 /                                         |                                                         |                                                      
|  |||    sec |- - --||                                                     |                                                         |                                                      
\  \\\        \2   4 //                                                     /                                                         /                                                      
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                              5                                                                                              

$$\frac{\left(\left(- \begin{cases} 0 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \frac{\pi}{2}\right) \bmod \pi = 0 \\- \frac{2 \sec{\left(\frac{b}{2} + \frac{\pi}{4} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{b}{2} + \frac{\pi}{4} \right)}}{\sec^{2}{\left(\frac{b}{2} - \frac{\pi}{4} \right)}}\right) \sec{\left(\frac{b}{2} - \frac{\pi}{4} \right)}} & \text{otherwise} \end{cases}\right) + \left(4 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(\pi - b\right) \bmod 2 \pi = 0 \\- \frac{1}{\sec{\left(b \right)}} & \text{otherwise} \end{cases}\right)\right)\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(b\right)} = 0 \wedge \left(b + \pi\right) \bmod 2 \pi = 0 \\- \sec{\left(b \right)} & \text{otherwise} \end{cases}\right)}{5}$$

3/5

$$\frac{3}{5}$$

Комбинаторика

3/5

$$\frac{3}{5}$$

Раскрыть выражение

3/5

$$\frac{3}{5}$$