Найти значение выражения cos(6*a)*cos(4*a)-sin(6*a)*sin(4*a)еслиa=4 (косинус от (6 умножить на a) умножить на косинус от (4 умножить на a) минус синус от (6 умножить на a) умножить на синус от (4 умножить на a)еслиa равно 4) [Есть ответ!]

cos(6*a)*cos(4*a)-sin(6*a)*sin(4*a)еслиa=4 (упростите выражение)

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Решение

Вы ввели [src]
cos(6*a)*cos(4*a) - sin(6*a)*sin(4*a)
$$- \sin{\left(4 a \right)} \sin{\left(6 a \right)} + \cos{\left(4 a \right)} \cos{\left(6 a \right)}$$
Подстановка условия [src]
cos(6*a)*cos(4*a) - sin(6*a)*sin(4*a) при a = 4
подставляем
cos(6*a)*cos(4*a) - sin(6*a)*sin(4*a)
$$- \sin{\left(4 a \right)} \sin{\left(6 a \right)} + \cos{\left(4 a \right)} \cos{\left(6 a \right)}$$
cos(4*a)*cos(6*a) - sin(4*a)*sin(6*a)
$$- \sin{\left(4 a \right)} \sin{\left(6 a \right)} + \cos{\left(4 a \right)} \cos{\left(6 a \right)}$$
переменные
a = 4
$$a = 4$$
cos(4*(4))*cos(6*(4)) - sin(4*(4))*sin(6*(4))
$$- \sin{\left(4 (4) \right)} \sin{\left(6 (4) \right)} + \cos{\left(4 (4) \right)} \cos{\left(6 (4) \right)}$$
cos(4*4)*cos(6*4) - sin(4*4)*sin(6*4)
$$\cos{\left(4 \cdot 4 \right)} \cos{\left(6 \cdot 4 \right)} - \sin{\left(4 \cdot 4 \right)} \sin{\left(6 \cdot 4 \right)}$$
cos(16)*cos(24) - sin(16)*sin(24)
$$\cos{\left(16 \right)} \cos{\left(24 \right)} - \sin{\left(16 \right)} \sin{\left(24 \right)}$$
Степени [src]
/ -6*I*a    6*I*a\ / -4*I*a    4*I*a\   /   -6*I*a    6*I*a\ /   -4*I*a    4*I*a\
|e         e     | |e         e     |   \- e       + e     /*\- e       + e     /
|------- + ------|*|------- + ------| + -----------------------------------------
\   2        2   / \   2        2   /                       4                    
$$\left(\frac{e^{4 i a}}{2} + \frac{e^{- 4 i a}}{2}\right) \left(\frac{e^{6 i a}}{2} + \frac{e^{- 6 i a}}{2}\right) + \frac{\left(e^{4 i a} - e^{- 4 i a}\right) \left(e^{6 i a} - e^{- 6 i a}\right)}{4}$$
Численный ответ [src]
cos(4*a)*cos(6*a) - sin(4*a)*sin(6*a)
Собрать выражение [src]
cos(10*a)
$$\cos{\left (10 a \right )}$$
Тригонометрическая часть [src]
cos(6*a)                    
-------- - sin(4*a)*sin(6*a)
sec(4*a)                    
$$- \sin{\left(4 a \right)} \sin{\left(6 a \right)} + \frac{\cos{\left(6 a \right)}}{\sec{\left(4 a \right)}}$$
//                           /           /pi      \           \\                                                                                                                                                                  
||        0           for And|im(a) = 0, |-- + 4*a| mod pi = 0||                                                                                                                                                                  
||                           \           \2       /           /| //      1         for And(im(a) = 0, 3*a mod pi = 0)\   //      0        for And(im(a) = 0, 4*a mod pi = 0)\ //      0        for And(im(a) = 0, 6*a mod pi = 0)\
||                                                             | ||                                                  |   ||                                                 | ||                                                 |
||      /      pi\                                             | ||        2                                         |   ||  2*cot(2*a)                                     | ||  2*cot(3*a)                                     |
|< 2*cot|2*a + --|                                             |*|<-1 + cot (3*a)                                    | - |<-------------              otherwise             |*|<-------------              otherwise             |
||      \      4 /                                             | ||--------------              otherwise             |   ||       2                                         | ||       2                                         |
||------------------                  otherwise                | ||       2                                          |   ||1 + cot (2*a)                                    | ||1 + cot (3*a)                                    |
||       2/      pi\                                           | \\1 + cot (3*a)                                     /   \\                                                 / \\                                                 /
||1 + cot |2*a + --|                                           |                                                                                                                                                                  
\\        \      4 /                                           /                                                                                                                                                                  
$$\left(- \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\frac{2 \cot{\left(2 a \right)}}{\cot^{2}{\left(2 a \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\frac{2 \cot{\left(3 a \right)}}{\cot^{2}{\left(3 a \right)} + 1} & \text{otherwise} \end{cases}\right)\right) + \left(\left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge \left(4 a + \frac{\pi}{2}\right) \bmod \pi = 0 \\\frac{2 \cot{\left(2 a + \frac{\pi}{4} \right)}}{\cot^{2}{\left(2 a + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\frac{\cot^{2}{\left(3 a \right)} - 1}{\cot^{2}{\left(3 a \right)} + 1} & \text{otherwise} \end{cases}\right)\right)$$
          1                      1        
---------------------- - -----------------
   /pi      \            csc(4*a)*csc(6*a)
csc|-- - 6*a|*sec(4*a)                    
   \2       /                             
$$\frac{1}{\csc{\left(- 6 a + \frac{\pi}{2} \right)} \sec{\left(4 a \right)}} - \frac{1}{\csc{\left(4 a \right)} \csc{\left(6 a \right)}}$$
//      1         for And(im(a) = 0, 2*a mod pi = 0)\                                                                                                                                                  
||                                                  |                                                                                                                                                  
||         1                                        |                                                                                                                                                  
||-1 + ---------                                    | //   1      for And(im(a) = 0, 3*a mod pi = 0)\   //   0      for And(im(a) = 0, 4*a mod pi = 0)\ //   0      for And(im(a) = 0, 6*a mod pi = 0)\
|<        2                                         |*|<                                            | - |<                                            |*|<                                            |
||     tan (2*a)                                    | \\cos(6*a)              otherwise             /   \\sin(4*a)              otherwise             / \\sin(6*a)              otherwise             /
||--------------              otherwise             |                                                                                                                                                  
||     2                                            |                                                                                                                                                  
\\  csc (2*a)                                       /                                                                                                                                                  
$$\left(- \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\sin{\left(4 a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\sin{\left(6 a \right)} & \text{otherwise} \end{cases}\right)\right) + \left(\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 2 a \bmod \pi = 0 \\\frac{-1 + \frac{1}{\tan^{2}{\left(2 a \right)}}}{\csc^{2}{\left(2 a \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\cos{\left(6 a \right)} & \text{otherwise} \end{cases}\right)\right)$$
//             1                for And(im(a) = 0, 2*a mod pi = 0)\                                                                                                                                                  
||                                                                |                                                                                                                                                  
||          /         2      \                                    | //   1      for And(im(a) = 0, 3*a mod pi = 0)\   //   0      for And(im(a) = 0, 4*a mod pi = 0)\ //   0      for And(im(a) = 0, 6*a mod pi = 0)\
|<   2      |      sin (4*a) |                                    |*|<                                            | - |<                                            |*|<                                            |
||sin (2*a)*|-1 + -----------|              otherwise             | \\cos(6*a)              otherwise             /   \\sin(4*a)              otherwise             / \\sin(6*a)              otherwise             /
||          |          4     |                                    |                                                                                                                                                  
\\          \     4*sin (2*a)/                                    /                                                                                                                                                  
$$\left(- \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\sin{\left(4 a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\sin{\left(6 a \right)} & \text{otherwise} \end{cases}\right)\right) + \left(\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 2 a \bmod \pi = 0 \\\left(-1 + \frac{\sin^{2}{\left(4 a \right)}}{4 \sin^{4}{\left(2 a \right)}}\right) \sin^{2}{\left(2 a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\cos{\left(6 a \right)} & \text{otherwise} \end{cases}\right)\right)$$
//            1               for And(im(a) = 0, 2*a mod pi = 0)\                                                                                                                                                                 
||                                                              |                                                                                                                                                                 
||     2    /         1    \                                    | //      1        for And(im(a) = 0, 3*a mod pi = 0)\   //      0        for And(im(a) = 0, 4*a mod pi = 0)\ //      0        for And(im(a) = 0, 6*a mod pi = 0)\
||4*tan (a)*|-1 + ---------|                                    | ||                                                 |   ||                                                 | ||                                                 |
||          |        2     |                                    | ||       2                                         |   ||  2*tan(2*a)                                     | ||  2*tan(3*a)                                     |
|<          \     tan (2*a)/                                    |*|<1 - tan (3*a)                                    | - |<-------------              otherwise             |*|<-------------              otherwise             |
||--------------------------              otherwise             | ||-------------              otherwise             |   ||       2                                         | ||       2                                         |
||                   2                                          | ||       2                                         |   ||1 + tan (2*a)                                    | ||1 + tan (3*a)                                    |
||      /       2   \                                           | \\1 + tan (3*a)                                    /   \\                                                 / \\                                                 /
||      \1 + tan (a)/                                           |                                                                                                                                                                 
\\                                                              /                                                                                                                                                                 
$$\left(- \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\frac{2 \tan{\left(2 a \right)}}{\tan^{2}{\left(2 a \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\frac{2 \tan{\left(3 a \right)}}{\tan^{2}{\left(3 a \right)} + 1} & \text{otherwise} \end{cases}\right)\right) + \left(\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 2 a \bmod \pi = 0 \\\frac{4 \left(-1 + \frac{1}{\tan^{2}{\left(2 a \right)}}\right) \tan^{2}{\left(a \right)}}{\left(\tan^{2}{\left(a \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\frac{1 - \tan^{2}{\left(3 a \right)}}{\tan^{2}{\left(3 a \right)} + 1} & \text{otherwise} \end{cases}\right)\right)$$
                                        /       2     \    /      pi\   
                                      2*\1 - tan (3*a)/*tan|2*a + --|   
        4*tan(2*a)*tan(3*a)                                \      4 /   
- ------------------------------- + ------------------------------------
  /       2     \ /       2     \   /       2     \ /       2/      pi\\
  \1 + tan (2*a)/*\1 + tan (3*a)/   \1 + tan (3*a)/*|1 + tan |2*a + --||
                                                    \        \      4 //
$$\frac{2 \cdot \left(1 - \tan^{2}{\left(3 a \right)}\right) \tan{\left(2 a + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(3 a \right)} + 1\right) \left(\tan^{2}{\left(2 a + \frac{\pi}{4} \right)} + 1\right)} - \frac{4 \tan{\left(2 a \right)} \tan{\left(3 a \right)}}{\left(\tan^{2}{\left(2 a \right)} + 1\right) \left(\tan^{2}{\left(3 a \right)} + 1\right)}$$
/      1         for And(im(a) = 0, 5*a mod pi = 0)
|                                                  
|        2                                         
<-1 + cot (5*a)                                    
|--------------              otherwise             
|       2                                          
\1 + cot (5*a)                                     
$$\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 5 a \bmod \pi = 0 \\\frac{\cot^{2}{\left(5 a \right)} - 1}{\cot^{2}{\left(5 a \right)} + 1} & \text{otherwise} \end{cases}$$
                       /      pi\    /      pi\
cos(4*a)*cos(6*a) - cos|4*a - --|*cos|6*a - --|
                       \      2 /    \      2 /
$$\cos{\left(4 a \right)} \cos{\left(6 a \right)} - \cos{\left(4 a - \frac{\pi}{2} \right)} \cos{\left(6 a - \frac{\pi}{2} \right)}$$
   cos(6*a)                      
------------- - sin(4*a)*sin(6*a)
   /pi      \                    
csc|-- - 4*a|                    
   \2       /                    
$$- \sin{\left(4 a \right)} \sin{\left(6 a \right)} + \frac{\cos{\left(6 a \right)}}{\csc{\left(- 4 a + \frac{\pi}{2} \right)}}$$
//            1               for And(im(a) = 0, 2*a mod pi = 0)\                                                                                                                                                  
||                                                              | //   1      for And(im(a) = 0, 3*a mod pi = 0)\   //   0      for And(im(a) = 0, 4*a mod pi = 0)\ //   0      for And(im(a) = 0, 6*a mod pi = 0)\
|<   2      /        2     \                                    |*|<                                            | - |<                                            |*|<                                            |
||sin (2*a)*\-1 + cot (2*a)/              otherwise             | \\cos(6*a)              otherwise             /   \\sin(4*a)              otherwise             / \\sin(6*a)              otherwise             /
\\                                                              /                                                                                                                                                  
$$\left(- \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\sin{\left(4 a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\sin{\left(6 a \right)} & \text{otherwise} \end{cases}\right)\right) + \left(\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 2 a \bmod \pi = 0 \\\left(\cot^{2}{\left(2 a \right)} - 1\right) \sin^{2}{\left(2 a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\cos{\left(6 a \right)} & \text{otherwise} \end{cases}\right)\right)$$
//         1           for And(im(a) = 0, 2*a mod pi = 0)\                                                                                                                                                       
||                                                       |                                                                                                                                                       
||          2                                            | //      1        for And(im(a) = 0, 3*a mod pi = 0)\                                                                                                  
||       csc (2*a)                                       | ||                                                 |   //   0      for And(im(a) = 0, 4*a mod pi = 0)\ //   0      for And(im(a) = 0, 6*a mod pi = 0)\
||-1 + --------------                                    | ||      1                                          |   ||                                            | ||                                            |
|<        2/pi      \                                    |*|<-------------              otherwise             | - |<   1                                        |*|<   1                                        |
||     csc |-- - 2*a|                                    | ||   /pi      \                                    |   ||--------              otherwise             | ||--------              otherwise             |
||         \2       /                                    | ||csc|-- - 6*a|                                    |   \\csc(4*a)                                    / \\csc(6*a)                                    /
||-------------------              otherwise             | \\   \2       /                                    /                                                                                                  
||        2                                              |                                                                                                                                                       
\\     csc (2*a)                                         /                                                                                                                                                       
$$\left(- \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\frac{1}{\csc{\left(4 a \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\frac{1}{\csc{\left(6 a \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 2 a \bmod \pi = 0 \\\frac{\frac{\csc^{2}{\left(2 a \right)}}{\csc^{2}{\left(- 2 a + \frac{\pi}{2} \right)}} - 1}{\csc^{2}{\left(2 a \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\frac{1}{\csc{\left(- 6 a + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right)$$
/       2     \ /       2     \                                  
\1 - tan (2*a)/*\1 - tan (3*a)/         4*tan(2*a)*tan(3*a)      
------------------------------- - -------------------------------
/       2     \ /       2     \   /       2     \ /       2     \
\1 + tan (2*a)/*\1 + tan (3*a)/   \1 + tan (2*a)/*\1 + tan (3*a)/
$$\frac{\left(1 - \tan^{2}{\left(2 a \right)}\right) \left(1 - \tan^{2}{\left(3 a \right)}\right)}{\left(\tan^{2}{\left(2 a \right)} + 1\right) \left(\tan^{2}{\left(3 a \right)} + 1\right)} - \frac{4 \tan{\left(2 a \right)} \tan{\left(3 a \right)}}{\left(\tan^{2}{\left(2 a \right)} + 1\right) \left(\tan^{2}{\left(3 a \right)} + 1\right)}$$
//         1           for And(im(a) = 0, 2*a mod pi = 0)\                                                                                                                                                            
||                                                       |                                                                                                                                                            
||        2/      pi\                                    |                                                                                                                                                            
||     sec |2*a - --|                                    |                                                   //      0        for And(im(a) = 0, 4*a mod pi = 0)\ //      0        for And(im(a) = 0, 6*a mod pi = 0)\
||         \      2 /                                    | //   1      for And(im(a) = 0, 3*a mod pi = 0)\   ||                                                 | ||                                                 |
||-1 + --------------                                    | ||                                            |   ||      1                                          | ||      1                                          |
|<          2                                            |*|<   1                                        | - |<-------------              otherwise             |*|<-------------              otherwise             |
||       sec (2*a)                                       | ||--------              otherwise             |   ||   /      pi\                                    | ||   /      pi\                                    |
||-------------------              otherwise             | \\sec(6*a)                                    /   ||sec|4*a - --|                                    | ||sec|6*a - --|                                    |
||      2/      pi\                                      |                                                   \\   \      2 /                                    / \\   \      2 /                                    /
||   sec |2*a - --|                                      |                                                                                                                                                            
||       \      2 /                                      |                                                                                                                                                            
\\                                                       /                                                                                                                                                            
$$\left(- \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\frac{1}{\sec{\left(4 a - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\frac{1}{\sec{\left(6 a - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)\right) + \left(\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 2 a \bmod \pi = 0 \\\frac{-1 + \frac{\sec^{2}{\left(2 a - \frac{\pi}{2} \right)}}{\sec^{2}{\left(2 a \right)}}}{\sec^{2}{\left(2 a - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\frac{1}{\sec{\left(6 a \right)}} & \text{otherwise} \end{cases}\right)\right)$$
    1    
---------
sec(10*a)
$$\frac{1}{\sec{\left(10 a \right)}}$$
   /pi      \    /pi      \                    
sin|-- + 4*a|*sin|-- + 6*a| - sin(4*a)*sin(6*a)
   \2       /    \2       /                    
$$- \sin{\left(4 a \right)} \sin{\left(6 a \right)} + \sin{\left(4 a + \frac{\pi}{2} \right)} \sin{\left(6 a + \frac{\pi}{2} \right)}$$
      1       
--------------
   /pi       \
csc|-- - 10*a|
   \2        /
$$\frac{1}{\csc{\left(- 10 a + \frac{\pi}{2} \right)}}$$
            /pi      \                    
cos(4*a)*sin|-- + 6*a| - sin(4*a)*sin(6*a)
            \2       /                    
$$- \sin{\left(4 a \right)} \sin{\left(6 a \right)} + \sin{\left(6 a + \frac{\pi}{2} \right)} \cos{\left(4 a \right)}$$
         2             2        -cos(10*a) + cos(2*a)        2         2     
1 - 2*cos (2*a) - 2*cos (3*a) - --------------------- + 4*cos (2*a)*cos (3*a)
                                          2                                  
$$- \frac{\cos{\left(2 a \right)} - \cos{\left(10 a \right)}}{2} + 4 \cos^{2}{\left(2 a \right)} \cos^{2}{\left(3 a \right)} - 2 \cos^{2}{\left(2 a \right)} - 2 \cos^{2}{\left(3 a \right)} + 1$$
             1                        1        
--------------------------- - -----------------
   /pi      \    /pi      \   csc(4*a)*csc(6*a)
csc|-- - 6*a|*csc|-- - 4*a|                    
   \2       /    \2       /                    
$$\frac{1}{\csc{\left(- 6 a + \frac{\pi}{2} \right)} \csc{\left(- 4 a + \frac{\pi}{2} \right)}} - \frac{1}{\csc{\left(4 a \right)} \csc{\left(6 a \right)}}$$
//                                  1                                     for And(im(a) = 0, 2*a mod pi = 0)\                                                                                                                                                                                                                                                                                 
||                                                                                                          | //                         1                           for And(im(a) = 0, 3*a mod pi = 0)\   //                        0                           for And(im(a) = 0, 4*a mod pi = 0)\ //                        0                           for And(im(a) = 0, 6*a mod pi = 0)\
||                 //      0         for And(im(a) = 0, 2*a mod pi = 0)\                                    | ||                                                                                       |   ||                                                                                      | ||                                                                                      |
||                 ||                                                  |                                    | ||/      1         for And(im(a) = 0, 3*a mod pi = 0)                                    |   ||/      0        for And(im(a) = 0, 4*a mod pi = 0)                                    | ||/      0        for And(im(a) = 0, 6*a mod pi = 0)                                    |
||                 ||       2                                          |                                    | |||                                                                                      |   |||                                                                                     | |||                                                                                     |
|
$$\left(- \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\frac{2 \cot{\left(2 a \right)}}{\cot^{2}{\left(2 a \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\frac{2 \cot{\left(3 a \right)}}{\cot^{2}{\left(3 a \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right) + \left(\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 2 a \bmod \pi = 0 \\\left(\cot^{2}{\left(2 a \right)} - 1\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 2 a \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(a \right)}}{\left(\cot^{2}{\left(a \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\frac{\cot^{2}{\left(3 a \right)} - 1}{\cot^{2}{\left(3 a \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right)$$
//      1         for And(im(a) = 0, 2*a mod pi = 0)\ //      1         for And(im(a) = 0, 3*a mod pi = 0)\   //      0        for And(im(a) = 0, 4*a mod pi = 0)\ //      0        for And(im(a) = 0, 6*a mod pi = 0)\
||                                                  | ||                                                  |   ||                                                 | ||                                                 |
||        2                                         | ||        2                                         |   ||  2*cot(2*a)                                     | ||  2*cot(3*a)                                     |
|<-1 + cot (2*a)                                    |*|<-1 + cot (3*a)                                    | - |<-------------              otherwise             |*|<-------------              otherwise             |
||--------------              otherwise             | ||--------------              otherwise             |   ||       2                                         | ||       2                                         |
||       2                                          | ||       2                                          |   ||1 + cot (2*a)                                    | ||1 + cot (3*a)                                    |
\\1 + cot (2*a)                                     / \\1 + cot (3*a)                                     /   \\                                                 / \\                                                 /
$$\left(- \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\frac{2 \cot{\left(2 a \right)}}{\cot^{2}{\left(2 a \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\frac{2 \cot{\left(3 a \right)}}{\cot^{2}{\left(3 a \right)} + 1} & \text{otherwise} \end{cases}\right)\right) + \left(\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 2 a \bmod \pi = 0 \\\frac{\cot^{2}{\left(2 a \right)} - 1}{\cot^{2}{\left(2 a \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\frac{\cot^{2}{\left(3 a \right)} - 1}{\cot^{2}{\left(3 a \right)} + 1} & \text{otherwise} \end{cases}\right)\right)$$
        1                        1             
----------------- - ---------------------------
sec(4*a)*sec(6*a)      /      pi\    /      pi\
                    sec|4*a - --|*sec|6*a - --|
                       \      2 /    \      2 /
$$- \frac{1}{\sec{\left(4 a - \frac{\pi}{2} \right)} \sec{\left(6 a - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(4 a \right)} \sec{\left(6 a \right)}}$$
   /pi       \
sin|-- + 10*a|
   \2        /
$$\sin{\left(10 a + \frac{\pi}{2} \right)}$$
        1                   1        
----------------- - -----------------
sec(4*a)*sec(6*a)   csc(4*a)*csc(6*a)
$$\frac{1}{\sec{\left(4 a \right)} \sec{\left(6 a \right)}} - \frac{1}{\csc{\left(4 a \right)} \csc{\left(6 a \right)}}$$
//             1                for And(im(a) = 0, 2*a mod pi = 0)\                                                                                                                                                       
||                                                                | //      1        for And(im(a) = 0, 3*a mod pi = 0)\                                                                                                  
||          /         2      \                                    | ||                                                 |   //   0      for And(im(a) = 0, 4*a mod pi = 0)\ //   0      for And(im(a) = 0, 6*a mod pi = 0)\
|<   2      |      sin (4*a) |                                    |*|<   /pi      \                                    | - |<                                            |*|<                                            |
||sin (2*a)*|-1 + -----------|              otherwise             | ||sin|-- + 6*a|              otherwise             |   \\sin(4*a)              otherwise             / \\sin(6*a)              otherwise             /
||          |          4     |                                    | \\   \2       /                                    /                                                                                                  
\\          \     4*sin (2*a)/                                    /                                                                                                                                                       
$$\left(- \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\sin{\left(4 a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\sin{\left(6 a \right)} & \text{otherwise} \end{cases}\right)\right) + \left(\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 2 a \bmod \pi = 0 \\\left(-1 + \frac{\sin^{2}{\left(4 a \right)}}{4 \sin^{4}{\left(2 a \right)}}\right) \sin^{2}{\left(2 a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\sin{\left(6 a + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)\right)$$
//            1               for And(im(a) = 0, 2*a mod pi = 0)\                                                                                                                                                  
||                                                              |                                                                                                                                                  
||   2      /         1    \                                    | //   1      for And(im(a) = 0, 3*a mod pi = 0)\   //   0      for And(im(a) = 0, 4*a mod pi = 0)\ //   0      for And(im(a) = 0, 6*a mod pi = 0)\
|
$$\left(- \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\sin{\left(4 a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\sin{\left(6 a \right)} & \text{otherwise} \end{cases}\right)\right) + \left(\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 2 a \bmod \pi = 0 \\\left(-1 + \frac{1}{\tan^{2}{\left(2 a \right)}}\right) \sin^{2}{\left(2 a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\cos{\left(6 a \right)} & \text{otherwise} \end{cases}\right)\right)$$
                                                                                                                               //      1         for And(im(a) = 0, 3*a mod pi = 0)\
                                                                                                                               ||                                                  |
                                                                                                              /        2     \ ||        2                                         |
                                                                                                              \-1 + cot (2*a)/*|<-1 + cot (3*a)                                    |
  //      0        for And(im(a) = 0, 4*a mod pi = 0)\ //      0        for And(im(a) = 0, 6*a mod pi = 0)\                    ||--------------              otherwise             |
  ||                                                 | ||                                                 |                    ||       2                                          |
  ||  2*cot(2*a)                                     | ||  2*cot(3*a)                                     |                    \\1 + cot (3*a)                                     /
- |<-------------              otherwise             |*|<-------------              otherwise             | + ----------------------------------------------------------------------
  ||       2                                         | ||       2                                         |                                      2                                  
  ||1 + cot (2*a)                                    | ||1 + cot (3*a)                                    |                               1 + cot (2*a)                             
  \\                                                 / \\                                                 /                                                                         
$$\left(\frac{\left(\cot^{2}{\left(2 a \right)} - 1\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\frac{\cot^{2}{\left(3 a \right)} - 1}{\cot^{2}{\left(3 a \right)} + 1} & \text{otherwise} \end{cases}\right)}{\cot^{2}{\left(2 a \right)} + 1}\right) - \left(\left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\frac{2 \cot{\left(2 a \right)}}{\cot^{2}{\left(2 a \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\frac{2 \cot{\left(3 a \right)}}{\cot^{2}{\left(3 a \right)} + 1} & \text{otherwise} \end{cases}\right)\right)$$
  //   0      for And(im(a) = 0, 4*a mod pi = 0)\ //   0      for And(im(a) = 0, 6*a mod pi = 0)\      2      /        2     \ //   1      for And(im(a) = 0, 3*a mod pi = 0)\
- |<                                            |*|<                                            | + sin (2*a)*\-1 + cot (2*a)/*|<                                            |
  \\sin(4*a)              otherwise             / \\sin(6*a)              otherwise             /                              \\cos(6*a)              otherwise             /
$$\left(\left(\cot^{2}{\left(2 a \right)} - 1\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\cos{\left(6 a \right)} & \text{otherwise} \end{cases}\right) \sin^{2}{\left(2 a \right)}\right) - \left(\left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\sin{\left(4 a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\sin{\left(6 a \right)} & \text{otherwise} \end{cases}\right)\right)$$
//                1                   for And(im(a) = 0, 2*a mod pi = 0)\                                                                                                                                                  
||                                                                      |                                                                                                                                                  
||     4       2    /         1    \                                    | //   1      for And(im(a) = 0, 3*a mod pi = 0)\   //   0      for And(im(a) = 0, 4*a mod pi = 0)\ //   0      for And(im(a) = 0, 6*a mod pi = 0)\
|<4*cos (a)*tan (a)*|-1 + ---------|              otherwise             |*|<                                            | - |<                                            |*|<                                            |
||                  |        2     |                                    | \\cos(6*a)              otherwise             /   \\sin(4*a)              otherwise             / \\sin(6*a)              otherwise             /
||                  \     tan (2*a)/                                    |                                                                                                                                                  
\\                                                                      /                                                                                                                                                  
$$\left(- \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\sin{\left(4 a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\sin{\left(6 a \right)} & \text{otherwise} \end{cases}\right)\right) + \left(\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 2 a \bmod \pi = 0 \\4 \left(-1 + \frac{1}{\tan^{2}{\left(2 a \right)}}\right) \cos^{4}{\left(a \right)} \tan^{2}{\left(a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\cos{\left(6 a \right)} & \text{otherwise} \end{cases}\right)\right)$$
/    1      for And(im(a) = 0, 5*a mod pi = 0)
<                                             
\cos(10*a)              otherwise             
$$\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 5 a \bmod \pi = 0 \\\cos{\left(10 a \right)} & \text{otherwise} \end{cases}$$
                                                                                                                //      1         for And(im(a) = 0, 3*a mod pi = 0)\              
                                                                                                                ||                                                  |              
                                                                                                                ||        2                                         |    /      pi\
                                                                                                              2*|<-1 + cot (3*a)                                    |*tan|2*a + --|
  //      0        for And(im(a) = 0, 4*a mod pi = 0)\ //      0        for And(im(a) = 0, 6*a mod pi = 0)\     ||--------------              otherwise             |    \      4 /
  ||                                                 | ||                                                 |     ||       2                                          |              
  ||  2*cot(2*a)                                     | ||  2*cot(3*a)                                     |     \\1 + cot (3*a)                                     /              
- |<-------------              otherwise             |*|<-------------              otherwise             | + ---------------------------------------------------------------------
  ||       2                                         | ||       2                                         |                                    2/      pi\                         
  ||1 + cot (2*a)                                    | ||1 + cot (3*a)                                    |                             1 + tan |2*a + --|                         
  \\                                                 / \\                                                 /                                     \      4 /                         
$$\left(- \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\frac{2 \cot{\left(2 a \right)}}{\cot^{2}{\left(2 a \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\frac{2 \cot{\left(3 a \right)}}{\cot^{2}{\left(3 a \right)} + 1} & \text{otherwise} \end{cases}\right)\right) + \left(\frac{2 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\frac{\cot^{2}{\left(3 a \right)} - 1}{\cot^{2}{\left(3 a \right)} + 1} & \text{otherwise} \end{cases}\right) \tan{\left(2 a + \frac{\pi}{4} \right)}}{\tan^{2}{\left(2 a + \frac{\pi}{4} \right)} + 1}\right)$$
       2     
1 - tan (5*a)
-------------
       2     
1 + tan (5*a)
$$\frac{1 - \tan^{2}{\left(5 a \right)}}{\tan^{2}{\left(5 a \right)} + 1}$$
                                                                                                      //   1      for And(im(a) = 0, 3*a mod pi = 0)\    /      pi\
                                                                                                    2*|<                                            |*tan|2*a + --|
  //   0      for And(im(a) = 0, 4*a mod pi = 0)\ //   0      for And(im(a) = 0, 6*a mod pi = 0)\     \\cos(6*a)              otherwise             /    \      4 /
- |<                                            |*|<                                            | + ---------------------------------------------------------------
  \\sin(4*a)              otherwise             / \\sin(6*a)              otherwise             /                                 2/      pi\                      
                                                                                                                           1 + tan |2*a + --|                      
                                                                                                                                   \      4 /                      
$$\left(- \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\sin{\left(4 a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\sin{\left(6 a \right)} & \text{otherwise} \end{cases}\right)\right) + \left(\frac{2 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\cos{\left(6 a \right)} & \text{otherwise} \end{cases}\right) \tan{\left(2 a + \frac{\pi}{4} \right)}}{\tan^{2}{\left(2 a + \frac{\pi}{4} \right)} + 1}\right)$$
cos(10*a)
$$\cos{\left(10 a \right)}$$
            /pi      \                    
cos(6*a)*sin|-- + 4*a| - sin(4*a)*sin(6*a)
            \2       /                    
$$- \sin{\left(4 a \right)} \sin{\left(6 a \right)} + \sin{\left(4 a + \frac{\pi}{2} \right)} \cos{\left(6 a \right)}$$
//                                 1                                    for And(im(a) = 0, 2*a mod pi = 0)\                                                                                                                                                                                                                                                                 
||                                                                                                        | //                      1                        for And(im(a) = 0, 3*a mod pi = 0)\   //                      0                        for And(im(a) = 0, 4*a mod pi = 0)\ //                      0                        for And(im(a) = 0, 6*a mod pi = 0)\
||                 //     0        for And(im(a) = 0, 2*a mod pi = 0)\                                    | ||                                                                                 |   ||                                                                                 | ||                                                                                 |
|
$$\left(- \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\sin{\left(4 a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\sin{\left(6 a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right) + \left(\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 2 a \bmod \pi = 0 \\\left(\cot^{2}{\left(2 a \right)} - 1\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 2 a \bmod \pi = 0 \\\frac{1 - \cos{\left(4 a \right)}}{2} & \text{otherwise} \end{cases}\right) & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\cos{\left(6 a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)\right)$$
//                 1                    for And(im(a) = 0, 2*a mod pi = 0)\                                                                                                                                                            
||                                                                        |                                                                                                                                                            
||               /          2        \                                    |                                                   //      0        for And(im(a) = 0, 4*a mod pi = 0)\ //      0        for And(im(a) = 0, 6*a mod pi = 0)\
||   2/      pi\ |       cos (2*a)   |                                    | //   1      for And(im(a) = 0, 3*a mod pi = 0)\   ||                                                 | ||                                                 |
|
$$\left(- \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\cos{\left(4 a - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\cos{\left(6 a - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)\right) + \left(\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 2 a \bmod \pi = 0 \\\left(\frac{\cos^{2}{\left(2 a \right)}}{\cos^{2}{\left(2 a - \frac{\pi}{2} \right)}} - 1\right) \cos^{2}{\left(2 a - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\cos{\left(6 a \right)} & \text{otherwise} \end{cases}\right)\right)$$
//                 /           /pi      \           \\                                                                                                                                                  
||   0      for And|im(a) = 0, |-- + 4*a| mod pi = 0|| //   1      for And(im(a) = 0, 3*a mod pi = 0)\   //   0      for And(im(a) = 0, 4*a mod pi = 0)\ //   0      for And(im(a) = 0, 6*a mod pi = 0)\
|<                 \           \2       /           /|*|<                                            | - |<                                            |*|<                                            |
||                                                   | \\cos(6*a)              otherwise             /   \\sin(4*a)              otherwise             / \\sin(6*a)              otherwise             /
\\cos(4*a)                  otherwise                /                                                                                                                                                  
$$\left(- \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 4 a \bmod \pi = 0 \\\sin{\left(4 a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 6 a \bmod \pi = 0 \\\sin{\left(6 a \right)} & \text{otherwise} \end{cases}\right)\right) + \left(\left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge \left(4 a + \frac{\pi}{2}\right) \bmod \pi = 0 \\\cos{\left(4 a \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge 3 a \bmod \pi = 0 \\\cos{\left(6 a \right)} & \text{otherwise} \end{cases}\right)\right)$$
Раскрыть выражение [src]
            8             4            2             10             6             2       6            2       2             2       4             2       8   
-1 - 640*cos (a) - 200*cos (a) + 26*cos (a) + 256*cos  (a) + 560*cos (a) - 384*cos (a)*sin (a) - 24*cos (a)*sin (a) + 176*cos (a)*sin (a) + 256*cos (a)*sin (a)
$$256 \sin^{8}{\left(a \right)} \cos^{2}{\left(a \right)} - 384 \sin^{6}{\left(a \right)} \cos^{2}{\left(a \right)} + 176 \sin^{4}{\left(a \right)} \cos^{2}{\left(a \right)} - 24 \sin^{2}{\left(a \right)} \cos^{2}{\left(a \right)} + 256 \cos^{10}{\left(a \right)} - 640 \cos^{8}{\left(a \right)} + 560 \cos^{6}{\left(a \right)} - 200 \cos^{4}{\left(a \right)} + 26 \cos^{2}{\left(a \right)} - 1$$