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Общий знаменатель 4*((-atan(sin(x)/(1+cos(x ... (2*sin(x))/(1+cos(x))-2))

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Примеры

Решение

Вы ввели [src]
  /     /  sin(x)  \                  \
  |-atan|----------|                  |
  |     \1 + cos(x)/          1       |
4*|------------------ - --------------|
  |        2             2*sin(x)     |
  |                     ---------- - 2|
  \                     1 + cos(x)    /
$$4 \left(\frac{1}{2} \left(-1 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )}\right) - \frac{1}{-2 + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}}\right)$$
Степени [src]
         4                /  sin(x)  \
- --------------- - 2*atan|----------|
        2*sin(x)          \1 + cos(x)/
  -2 + ----------                     
       1 + cos(x)
$$- 2 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} - \frac{4}{-2 + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}}$$
Численный ответ [src]
-2.0*atan(sin(x)/(1 + cos(x))) - 4.0/(-2.0 + 2.0*sin(x)/(1.0 + cos(x)))
Рациональный знаменатель [src]
          /  sin(x)  \                    /  sin(x)  \                /  sin(x)  \       
2 - 2*atan|----------| + 2*cos(x) - 2*atan|----------|*cos(x) + 2*atan|----------|*sin(x)
          \1 + cos(x)/                    \1 + cos(x)/                \1 + cos(x)/       
-----------------------------------------------------------------------------------------
                                   1 - sin(x) + cos(x)
$$\frac{1}{- \sin{\left (x \right )} + \cos{\left (x \right )} + 1} \left(2 \sin{\left (x \right )} \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} - 2 \cos{\left (x \right )} \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} + 2 \cos{\left (x \right )} - 2 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} + 2\right)$$
Объединение рациональных выражений [src]
  /                                         /  sin(x)  \\
2*|-1 - cos(x) - (-1 - cos(x) + sin(x))*atan|----------||
  \                                         \1 + cos(x)//
---------------------------------------------------------
                   -1 - cos(x) + sin(x)
$$\frac{1}{\sin{\left (x \right )} - \cos{\left (x \right )} - 1} \left(- 2 \left(\sin{\left (x \right )} - \cos{\left (x \right )} - 1\right) \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} - 2 \cos{\left (x \right )} - 2\right)$$
Общее упрощение [src]
        /  sin(x)  \         4       
- 2*atan|----------| + --------------
        \1 + cos(x)/        2*sin(x) 
                       2 - ----------
                           1 + cos(x)
$$- 2 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} + \frac{4}{2 - \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}}$$
Собрать выражение [src]
                                                                 /  sin(x)  \            /  sin(x)  \                /  sin(x)  \       
                                                           4*atan|----------|      4*atan|----------|*sin(x)   4*atan|----------|*cos(x)
             4                       4*cos(x)                    \1 + cos(x)/            \1 + cos(x)/                \1 + cos(x)/       
- ------------------------ - ------------------------ + ------------------------ - ------------------------- + -------------------------
  -2 - 2*cos(x) + 2*sin(x)   -2 - 2*cos(x) + 2*sin(x)   -2 - 2*cos(x) + 2*sin(x)    -2 - 2*cos(x) + 2*sin(x)    -2 - 2*cos(x) + 2*sin(x)
$$- \frac{4 \sin{\left (x \right )} \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )}}{2 \sin{\left (x \right )} - 2 \cos{\left (x \right )} - 2} + \frac{4 \cos{\left (x \right )} \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )}}{2 \sin{\left (x \right )} - 2 \cos{\left (x \right )} - 2} - \frac{4 \cos{\left (x \right )}}{2 \sin{\left (x \right )} - 2 \cos{\left (x \right )} - 2} + \frac{4 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )}}{2 \sin{\left (x \right )} - 2 \cos{\left (x \right )} - 2} - \frac{4}{2 \sin{\left (x \right )} - 2 \cos{\left (x \right )} - 2}$$
                     /     /  sin(x)  \\
                   4*|-atan|----------||
        4            \     \1 + cos(x)//
- -------------- + ---------------------
   2*sin(x)                  2          
  ---------- - 2                        
  1 + cos(x)
$$\frac{1}{2} \left(-1 \cdot 4 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )}\right) - \frac{4}{-2 + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}}$$
Общий знаменатель [src]
          /  sin(x)  \         2*sin(x)     
2 - 2*atan|----------| + -------------------
          \1 + cos(x)/   1 - sin(x) + cos(x)
$$- 2 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} + 2 + \frac{2 \sin{\left (x \right )}}{- \sin{\left (x \right )} + \cos{\left (x \right )} + 1}$$
Тригонометрическая часть [src]
         4                /  sin(x)  \
- --------------- - 2*atan|----------|
        2*sin(x)          \1 + cos(x)/
  -2 + ----------                     
       1 + cos(x)
$$- 2 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} - \frac{4}{-2 + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}}$$
Комбинаторика [src]
   /                  /  sin(x)  \              /  sin(x)  \              /  sin(x)  \\
-2*|-1 - cos(x) + atan|----------|*cos(x) - atan|----------|*sin(x) + atan|----------||
   \                  \1 + cos(x)/              \1 + cos(x)/              \1 + cos(x)//
---------------------------------------------------------------------------------------
                                  1 - sin(x) + cos(x)
$$- \frac{1}{- \sin{\left (x \right )} + \cos{\left (x \right )} + 1} \left(- 2 \sin{\left (x \right )} \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} + 2 \cos{\left (x \right )} \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} - 2 \cos{\left (x \right )} + 2 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} - 2\right)$$
Раскрыть выражение [src]
         4                /  sin(x)  \
- --------------- - 2*atan|----------|
        2*sin(x)          \1 + cos(x)/
  -2 + ----------                     
       1 + cos(x)
$$- 2 \operatorname{atan}{\left (\frac{\sin{\left (x \right )}}{\cos{\left (x \right )} + 1} \right )} - \frac{4}{-2 + \frac{2 \sin{\left (x \right )}}{\cos{\left (x \right )} + 1}}$$