cos(t)^2-(cot(t)^2+1)*sin(t)^2еслиt=-1/4 (упростите выражение)

Вы ввели

   2      /   2       \    2   
cos (t) - \cot (t) + 1/*sin (t)

$$- \left(\cot^{2}{\left(t \right)} + 1\right) \sin^{2}{\left(t \right)} + \cos^{2}{\left(t \right)}$$

Подстановка условия

cos(t)^2 - (cot(t)^2 + 1)*sin(t)^2 при t = -1/4

подставляем

   2      /   2       \    2   
cos (t) - \cot (t) + 1/*sin (t)

$$- \left(\cot^{2}{\left(t \right)} + 1\right) \sin^{2}{\left(t \right)} + \cos^{2}{\left(t \right)}$$

    2   
-sin (t)

$$- \sin^{2}{\left(t \right)}$$

переменные

t = -1/4

$$t = - \frac{1}{4}$$

    2        
-sin ((-1/4))

$$- \sin^{2}{\left((-1/4) \right)}$$

    2      
-sin (-1/4)

$$- \sin^{2}{\left(- \frac{1}{4} \right)}$$

    2     
-sin (1/4)

$$- \sin^{2}{\left(\frac{1}{4} \right)}$$

Степени

   2         2    /        2   \
cos (t) + sin (t)*\-1 - cot (t)/

$$\left(- \cot^{2}{\left(t \right)} - 1\right) \sin^{2}{\left(t \right)} + \cos^{2}{\left(t \right)}$$

              2                   2              
/ I*t    -I*t\    /   -I*t    I*t\  /       2   \
|e      e    |    \- e     + e   / *\1 + cot (t)/
|---- + -----|  + -------------------------------
\ 2       2  /                   4               

$$\left(\frac{e^{i t}}{2} + \frac{e^{- i t}}{2}\right)^{2} + \frac{\left(e^{i t} - e^{- i t}\right)^{2} \left(\cot^{2}{\left(t \right)} + 1\right)}{4}$$

Численный ответ

cos(t)^2 - sin(t)^2*(1.0 + cot(t)^2)

Рациональный знаменатель

   2         2         2       2   
cos (t) - sin (t) - cot (t)*sin (t)

$$- \sin^{2}{\left(t \right)} \cot^{2}{\left(t \right)} - \sin^{2}{\left(t \right)} + \cos^{2}{\left(t \right)}$$

Общее упрощение

    2   
-sin (t)

$$- \sin^{2}{\left(t \right)}$$

Собрать выражение

                  2         2            
1   cos(2*t)   csc (t)   csc (t)*cos(2*t)
- + -------- - ------- + ----------------
2      2          2             2        

$$\frac{1}{2} \cos{\left (2 t \right )} \csc^{2}{\left (t \right )} + \frac{1}{2} \cos{\left (2 t \right )} - \frac{1}{2} \csc^{2}{\left (t \right )} + \frac{1}{2}$$

Общий знаменатель

   2         2         2       2   
cos (t) - sin (t) - cot (t)*sin (t)

$$- \sin^{2}{\left(t \right)} \cot^{2}{\left(t \right)} - \sin^{2}{\left(t \right)} + \cos^{2}{\left(t \right)}$$

Тригонометрическая часть

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

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

  -1   
-------
   2   
csc (t)

$$- \frac{1}{\csc^{2}{\left(t \right)}}$$

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

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

                       /       2     \
   2/    pi\      2    |    sin (2*t)|
sin |t + --| - sin (t)*|1 + ---------|
    \    2 /           |         4   |
                       \    4*sin (t)/

$$- \left(1 + \frac{\sin^{2}{\left(2 t \right)}}{4 \sin^{4}{\left(t \right)}}\right) \sin^{2}{\left(t \right)} + \sin^{2}{\left(t + \frac{\pi}{2} \right)}$$

                 2   
              csc (t)
          1 + -------
                 2   
   1          sec (t)
------- - -----------
   2           2     
sec (t)     csc (t)  

$$- \frac{\frac{\csc^{2}{\left(t \right)}}{\sec^{2}{\left(t \right)}} + 1}{\csc^{2}{\left(t \right)}} + \frac{1}{\sec^{2}{\left(t \right)}}$$

                 2/    pi\
              sec |t - --|
                  \    2 /
          1 + ------------
                   2      
   1            sec (t)   
------- - ----------------
   2           2/    pi\  
sec (t)     sec |t - --|  
                \    2 /  

$$- \frac{1 + \frac{\sec^{2}{\left(t - \frac{\pi}{2} \right)}}{\sec^{2}{\left(t \right)}}}{\sec^{2}{\left(t - \frac{\pi}{2} \right)}} + \frac{1}{\sec^{2}{\left(t \right)}}$$

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

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

                  /       2     \
   2         2    |    sin (2*t)|
cos (t) - sin (t)*|1 + ---------|
                  |         4   |
                  \    4*sin (t)/

$$- \left(1 + \frac{\sin^{2}{\left(2 t \right)}}{4 \sin^{4}{\left(t \right)}}\right) \sin^{2}{\left(t \right)} + \cos^{2}{\left(t \right)}$$

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

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

    2   
-sin (t)

$$- \sin^{2}{\left(t \right)}$$

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

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

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

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

                        2      
                     csc (t)   
               1 + ------------
                      2/pi    \
                   csc |-- - t|
     1                 \2     /
------------ - ----------------
   2/pi    \          2        
csc |-- - t|       csc (t)     
    \2     /                   

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

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

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

    2/    pi\
-cos |t - --|
     \    2 /

$$- \cos^{2}{\left(t - \frac{\pi}{2} \right)}$$

             2        2/t\ /       1   \
/       2/t\\    4*tan |-|*|1 + -------|
|1 - tan |-||          \2/ |       2   |
\        \2//              \    tan (t)/
-------------- - -----------------------
             2                     2    
/       2/t\\         /       2/t\\     
|1 + tan |-||         |1 + tan |-||     
\        \2//         \        \2//     

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

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

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

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

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

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

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

  1   cos(2*t)
- - + --------
  2      2    

$$\frac{\cos{\left(2 t \right)}}{2} - \frac{1}{2}$$

                  /       2   \
   2         2    |    cos (t)|
cos (t) - sin (t)*|1 + -------|
                  |       2   |
                  \    sin (t)/

$$- \left(1 + \frac{\cos^{2}{\left(t \right)}}{\sin^{2}{\left(t \right)}}\right) \sin^{2}{\left(t \right)} + \cos^{2}{\left(t \right)}$$

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

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

                       /         2      \
   2         2/    pi\ |      cos (t)   |
cos (t) - cos |t - --|*|1 + ------------|
              \    2 / |       2/    pi\|
                       |    cos |t - --||
                       \        \    2 //

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

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

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

 //   0     for And(im(t) = 0, t mod pi = 0)\
 ||                                         |
-|<   2                                     |
 ||sin (t)             otherwise            |
 \\                                         /

$$- \begin{cases} 0 & \text{for}\: \operatorname{im}{\left(t\right)} = 0 \wedge t \bmod \pi = 0 \\\sin^{2}{\left(t \right)} & \text{otherwise} \end{cases}$$

    -1      
------------
   2/    pi\
sec |t - --|
    \    2 /

$$- \frac{1}{\sec^{2}{\left(t - \frac{\pi}{2} \right)}}$$

        2/t\  
  -4*tan |-|  
         \2/  
--------------
             2
/       2/t\\ 
|1 + tan |-|| 
\        \2// 

$$- \frac{4 \tan^{2}{\left(\frac{t}{2} \right)}}{\left(\tan^{2}{\left(\frac{t}{2} \right)} + 1\right)^{2}}$$

Комбинаторика

   2         2         2       2   
cos (t) - sin (t) - cot (t)*sin (t)

$$- \sin^{2}{\left(t \right)} \cot^{2}{\left(t \right)} - \sin^{2}{\left(t \right)} + \cos^{2}{\left(t \right)}$$

Раскрыть выражение

   2         2         2       2   
cos (t) - sin (t) - cot (t)*sin (t)

$$- \sin^{2}{\left(t \right)} \cot^{2}{\left(t \right)} - \sin^{2}{\left(t \right)} + \cos^{2}{\left(t \right)}$$