Господин Экзамен

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Упрощение выражений/ cot(pi-x) если x=-3

cot(pi-x) если x=-3

Выражение, которое надо упростить:

Решение

Вы ввели [src] 
cot(pi - x)
$$\cot{\left(- x + \pi \right)}$$ 
cot(pi - x)
Общее упрощение [src] 
-cot(x)
$$- \cot{\left(x \right)}$$ 
-cot(x)
Подстановка условия [src] 
cot(pi - x) при x = -3
подставляем
cot(pi - x)
$$\cot{\left(- x + \pi \right)}$$ 
-cot(x)
$$- \cot{\left(x \right)}$$ 
переменные
x = -3
$$x = -3$$ 
-cot((-3))
$$- \cot{\left((-3) \right)}$$ 
-cot(-3)
$$- \cot{\left(-3 \right)}$$ 
cot(3)
$$\cot{\left(3 \right)}$$ 
cot(3)
Объединение рациональных выражений [src] 
-cot(x)
$$- \cot{\left(x \right)}$$ 
-cot(x)
Численный ответ [src] 
cot(pi - x)
cot(pi - x)
Общий знаменатель [src] 
-cot(x)
$$- \cot{\left(x \right)}$$ 
-cot(x)
Степени [src] 
-cot(x)
$$- \cot{\left(x \right)}$$ 
-cot(x)
Рациональный знаменатель [src] 
-cot(x)
$$- \cot{\left(x \right)}$$ 
-cot(x)
Комбинаторика [src] 
-cot(x)
$$- \cot{\left(x \right)}$$ 
-cot(x)
Собрать выражение [src] 
-cot(x)
$$- \cot{\left(x \right)}$$ 
-cot(x)
Раскрыть выражение [src] 
-cot(x)
$$- \cot{\left(x \right)}$$ 
       1          zoo*cot(x) 
- ------------ + ------------
  zoo - cot(x)   zoo - cot(x)
$$\frac{\tilde{\infty} \cot{\left(x \right)}}{- \cot{\left(x \right)} + \tilde{\infty}} - \frac{1}{- \cot{\left(x \right)} + \tilde{\infty}}$$ 
-1/(±oo - cot(x)) + ±oo*cot(x)/(±oo - cot(x))
Тригонометрическая часть [src] 
-cot(x)
$$- \cot{\left(x \right)}$$ 
 -1   
------
tan(x)
$$- \frac{1}{\tan{\left(x \right)}}$$ 
-csc(x) 
--------
 sec(x)
$$- \frac{\csc{\left(x \right)}}{\sec{\left(x \right)}}$$ 
-cos(x) 
--------
 sin(x)
$$- \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$$ 
-sin(2*x) 
----------
     2    
2*sin (x)
$$- \frac{\sin{\left(2 x \right)}}{2 \sin^{2}{\left(x \right)}}$$ 
    2     
-csc (x)  
----------
2*csc(2*x)
$$- \frac{\csc^{2}{\left(x \right)}}{2 \csc{\left(2 x \right)}}$$ 
  -cos(x)  
-----------
   /    pi\
cos|x - --|
   \    2 /
$$- \frac{\cos{\left(x \right)}}{\cos{\left(x - \frac{\pi}{2} \right)}}$$ 
    /    pi\ 
-sin|x + --| 
    \    2 / 
-------------
    sin(x)
$$- \frac{\sin{\left(x + \frac{\pi}{2} \right)}}{\sin{\left(x \right)}}$$ 
    /    pi\ 
-sec|x - --| 
    \    2 / 
-------------
    sec(x)
$$- \frac{\sec{\left(x - \frac{\pi}{2} \right)}}{\sec{\left(x \right)}}$$ 
    /pi    \ 
-sec|-- - x| 
    \2     / 
-------------
    sec(x)
$$- \frac{\sec{\left(- x + \frac{\pi}{2} \right)}}{\sec{\left(x \right)}}$$ 
  -csc(x)  
-----------
   /pi    \
csc|-- - x|
   \2     /
$$- \frac{\csc{\left(x \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}}$$ 
 /          2/x\\ 
-|-1 + 2*cos |-|| 
 \           \2// 
------------------
      sin(x)
$$- \frac{2 \cos^{2}{\left(\frac{x}{2} \right)} - 1}{\sin{\left(x \right)}}$$ 
-csc(pi - x) 
-------------
    /pi    \ 
 csc|-- - x| 
    \2     /
$$- \frac{\csc{\left(- x + \pi \right)}}{\csc{\left(- x + \frac{\pi}{2} \right)}}$$ 
 /       2/x\\ 
-|1 - tan |-|| 
 \        \2// 
---------------
         /x\   
    2*tan|-|   
         \2/
$$- \frac{- \tan^{2}{\left(\frac{x}{2} \right)} + 1}{2 \tan{\left(\frac{x}{2} \right)}}$$ 
   /x\           
tan|-|           
   \2/      1    
------ - --------
  2           /x\
         2*tan|-|
              \2/
$$\frac{\tan{\left(\frac{x}{2} \right)}}{2} - \frac{1}{2 \tan{\left(\frac{x}{2} \right)}}$$ 
     2/    pi\ 
 -sec |x - --| 
      \    2 / 
---------------
     /      pi\
2*sec|2*x - --|
     \      2 /
$$- \frac{\sec^{2}{\left(x - \frac{\pi}{2} \right)}}{2 \sec{\left(2 x - \frac{\pi}{2} \right)}}$$ 
    /      pi\ 
-cos|2*x - --| 
    \      2 / 
---------------
      2/    pi\
 2*cos |x - --|
       \    2 /
$$- \frac{\cos{\left(2 x - \frac{\pi}{2} \right)}}{2 \cos^{2}{\left(x - \frac{\pi}{2} \right)}}$$ 
              2        
 /       2/x\\         
-|1 + tan |-|| *tan(x) 
 \        \2//         
-----------------------
  /       2   \    2/x\
4*\1 + tan (x)/*tan |-|
                    \2/
$$- \frac{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \tan{\left(x \right)}}{4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(\frac{x}{2} \right)}}$$ 
 /       2/x\\    /x   pi\ 
-|1 + cot |-||*tan|- + --| 
 \        \2//    \2   4 / 
---------------------------
 /       2/x   pi\\    /x\ 
 |1 + tan |- + --||*cot|-| 
 \        \2   4 //    \2/
$$- \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \tan{\left(\frac{x}{2} + \frac{\pi}{4} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1\right) \cot{\left(\frac{x}{2} \right)}}$$ 
 /       2/x   pi\\ /        2/x\\ 
-|1 + tan |- + --||*|-1 + cot |-|| 
 \        \2   4 // \         \2// 
-----------------------------------
 /       2/x\\ /        2/x   pi\\ 
 |1 + cot |-||*|-1 + tan |- + --|| 
 \        \2// \         \2   4 //
$$- \frac{\left(\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)}{\left(\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} - 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$ 
 /       2/x   pi\\ /       2/x\\ 
-|1 + cot |- + --||*|1 - tan |-|| 
 \        \2   4 // \        \2// 
----------------------------------
 /       2/x\\ /       2/x   pi\\ 
 |1 + tan |-||*|1 - cot |- + --|| 
 \        \2// \        \2   4 //
$$- \frac{\left(- \tan^{2}{\left(\frac{x}{2} \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1\right)}{\left(- \cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)}$$ 
                                 //  zoo    for x mod pi = 0\ 
                                 ||                         | 
 //   0      for 2*x mod pi = 0\ ||   1                     | 
-|<                            |*|<-------     otherwise    | 
 \\sin(2*x)      otherwise     / ||   2                     | 
                                 ||sin (x)                  | 
                                 \\                         / 
--------------------------------------------------------------
                              2
$$- \frac{\left(\begin{cases} 0 & \text{for}\: 2 x \bmod \pi = 0 \\\sin{\left(2 x \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: x \bmod \pi = 0 \\\frac{1}{\sin^{2}{\left(x \right)}} & \text{otherwise} \end{cases}\right)}{2}$$ 
                               //                     /    3*pi\             \
                               ||       1         for |x + ----| mod 2*pi = 0|
                               ||                     \     2  /             |
                               ||                                            |
 //  1     for x mod 2*pi = 0\ ||  1         /x\                             |
-|<                          |*|<------ + tan|-|                             |
 \\cos(x)      otherwise     / ||   /x\      \2/                             |
                               ||tan|-|                                      |
                               ||   \2/                                      |
                               ||---------------           otherwise         |
                               \\       2                                    /
$$- \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\cos{\left(x \right)} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \left(x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan{\left(\frac{x}{2} \right)} + \frac{1}{\tan{\left(\frac{x}{2} \right)}}}{2} & \text{otherwise} \end{cases}\right)$$ 
                                    //     zoo        for x mod pi = 0\ 
                                    ||                                | 
 //     0       for 2*x mod pi = 0\ ||             2                  | 
 ||                               | ||/       2/x\\                   | 
 ||  2*cot(x)                     | |||1 + cot |-||                   | 
-|<-----------      otherwise     |*|<\        \2//                   | 
 ||       2                       | ||--------------     otherwise    | 
 ||1 + cot (x)                    | ||       2/x\                     | 
 \\                               / ||  4*cot |-|                     | 
                                    ||        \2/                     | 
                                    \\                                / 
------------------------------------------------------------------------
                                   2
$$- \frac{\left(\begin{cases} 0 & \text{for}\: 2 x \bmod \pi = 0 \\\frac{2 \cot{\left(x \right)}}{\cot^{2}{\left(x \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} \tilde{\infty} & \text{for}\: x \bmod \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2}}{4 \cot^{2}{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases}\right)}{2}$$ 
                                     //                       /    3*pi\             \
 //     1        for x mod 2*pi = 0\ ||        1          for |x + ----| mod 2*pi = 0|
 ||                                | ||                       \     2  /             |
 ||        2/x\                    | ||                                              |
 ||-1 + cot |-|                    | ||        2/x   pi\                             |
-|<         \2/                    |*|< 1 + tan |- + --|                             |
 ||------------      otherwise     | ||         \2   4 /                             |
 ||       2/x\                     | ||-----------------           otherwise         |
 ||1 + cot |-|                     | ||        2/x   pi\                             |
 \\        \2/                     / ||-1 + tan |- + --|                             |
                                     \\         \2   4 /                             /
$$- \left(\begin{cases} 1 & \text{for}\: x \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) \left(\begin{cases} 1 & \text{for}\: \left(x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1}{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} - 1} & \text{otherwise} \end{cases}\right)$$ 
-Piecewise((1, Mod(x = 2*pi, 0)), ((-1 + cot(x/2)^2)/(1 + cot(x/2)^2), True))*Piecewise((1, Mod(x + 3*pi/2 = 2*pi, 0)), ((1 + tan(x/2 + pi/4)^2)/(-1 + tan(x/2 + pi/4)^2), True))
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