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

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Примеры

Решение

Вы ввели [src]
-4*cos(2*x)   2*(1 - 2*sin(2*x))*cos(x)*sin(x)
----------- + --------------------------------
       2                            2         
1 + cos (x)            /       2   \          
                       \1 + cos (x)/
$$\frac{\sin{\left (x \right )}}{\left(\cos^{2}{\left (x \right )} + 1\right)^{2}} 2 \left(- 2 \sin{\left (2 x \right )} + 1\right) \cos{\left (x \right )} + \frac{-1 \cdot 4 \cos{\left (2 x \right )}}{\cos^{2}{\left (x \right )} + 1}$$
Степени [src]
   4*cos(2*x)   (2 - 4*sin(2*x))*cos(x)*sin(x)
- ----------- + ------------------------------
         2                           2        
  1 + cos (x)           /       2   \         
                        \1 + cos (x)/
$$\frac{\sin{\left (x \right )} \cos{\left (x \right )}}{\left(\cos^{2}{\left (x \right )} + 1\right)^{2}} \left(- 4 \sin{\left (2 x \right )} + 2\right) - \frac{4 \cos{\left (2 x \right )}}{\cos^{2}{\left (x \right )} + 1}$$
Численный ответ [src]
-4.0*cos(2*x)/(1.0 + cos(x)^2) + 2.0*(1.0 - 2.0*sin(2*x))*cos(x)*sin(x)/(1.0 + cos(x)^2)^2
Рациональный знаменатель [src]
                 2                                                        
    /       2   \             /       2   \                               
- 4*\1 + cos (x)/ *cos(2*x) + \1 + cos (x)/*(2 - 4*sin(2*x))*cos(x)*sin(x)
--------------------------------------------------------------------------
                                           3                              
                              /       2   \                               
                              \1 + cos (x)/
$$\frac{1}{\left(\cos^{2}{\left (x \right )} + 1\right)^{3}} \left(\left(- 4 \sin{\left (2 x \right )} + 2\right) \left(\cos^{2}{\left (x \right )} + 1\right) \sin{\left (x \right )} \cos{\left (x \right )} - 4 \left(\cos^{2}{\left (x \right )} + 1\right)^{2} \cos{\left (2 x \right )}\right)$$
Объединение рациональных выражений [src]
  /    /       2   \                                          \
2*\- 2*\1 + cos (x)/*cos(2*x) + (1 - 2*sin(2*x))*cos(x)*sin(x)/
---------------------------------------------------------------
                                      2                        
                         /       2   \                         
                         \1 + cos (x)/
$$\frac{1}{\left(\cos^{2}{\left (x \right )} + 1\right)^{2}} \left(2 \left(- 2 \sin{\left (2 x \right )} + 1\right) \sin{\left (x \right )} \cos{\left (x \right )} - 4 \left(\cos^{2}{\left (x \right )} + 1\right) \cos{\left (2 x \right )}\right)$$
Общее упрощение [src]
4*(-2 - 6*cos(2*x) + sin(2*x))
------------------------------
                     2        
       (3 + cos(2*x))
$$\frac{1}{\left(\cos{\left (2 x \right )} + 3\right)^{2}} \left(4 \sin{\left (2 x \right )} - 24 \cos{\left (2 x \right )} - 8\right)$$
Собрать выражение [src]
               8                 8*cos(2*x)             8*cos(4*x)                    8*sin(2*x)        
- --------------------------- - ------------ + --------------------------- + ---------------------------
  19 + 12*cos(2*x) + cos(4*x)   3 + cos(2*x)   19 + 12*cos(2*x) + cos(4*x)   19 + 12*cos(2*x) + cos(4*x)
$$\frac{8 \sin{\left (2 x \right )}}{12 \cos{\left (2 x \right )} + \cos{\left (4 x \right )} + 19} + \frac{8 \cos{\left (4 x \right )}}{12 \cos{\left (2 x \right )} + \cos{\left (4 x \right )} + 19} - \frac{8}{12 \cos{\left (2 x \right )} + \cos{\left (4 x \right )} + 19} - \frac{8 \cos{\left (2 x \right )}}{\cos{\left (2 x \right )} + 3}$$
Общий знаменатель [src]
 /                                    2                                       \ 
-\4*cos(2*x) - 2*cos(x)*sin(x) + 4*cos (x)*cos(2*x) + 4*cos(x)*sin(x)*sin(2*x)/ 
--------------------------------------------------------------------------------
                                   4           2                                
                            1 + cos (x) + 2*cos (x)
$$- \frac{1}{\cos^{4}{\left (x \right )} + 2 \cos^{2}{\left (x \right )} + 1} \left(4 \sin{\left (x \right )} \sin{\left (2 x \right )} \cos{\left (x \right )} - 2 \sin{\left (x \right )} \cos{\left (x \right )} + 4 \cos^{2}{\left (x \right )} \cos{\left (2 x \right )} + 4 \cos{\left (2 x \right )}\right)$$
Тригонометрическая часть [src]
-1 + cos(4*x) + sin(2*x)    4*cos(2*x)
------------------------ - -----------
                  2               2   
    /        2   \         1 + cos (x)
    \-2 + sin (x)/
$$- \frac{4 \cos{\left (2 x \right )}}{\cos^{2}{\left (x \right )} + 1} + \frac{1}{\left(\sin^{2}{\left (x \right )} - 2\right)^{2}} \left(\sin{\left (2 x \right )} + \cos{\left (4 x \right )} - 1\right)$$
Комбинаторика [src]
   /                                  2                                       \
-2*\2*cos(2*x) - cos(x)*sin(x) + 2*cos (x)*cos(2*x) + 2*cos(x)*sin(x)*sin(2*x)/
-------------------------------------------------------------------------------
                                              2                                
                                 /       2   \                                 
                                 \1 + cos (x)/
$$- \frac{1}{\left(\cos^{2}{\left (x \right )} + 1\right)^{2}} \left(4 \sin{\left (x \right )} \sin{\left (2 x \right )} \cos{\left (x \right )} - 2 \sin{\left (x \right )} \cos{\left (x \right )} + 4 \cos^{2}{\left (x \right )} \cos{\left (2 x \right )} + 4 \cos{\left (2 x \right )}\right)$$
Раскрыть выражение [src]
         2           2                                           
  - 4*sin (x) + 4*cos (x)   2*(1 - 4*cos(x)*sin(x))*cos(x)*sin(x)
- ----------------------- + -------------------------------------
               2                                     2           
        1 + cos (x)                     /       2   \            
                                        \1 + cos (x)/
$$\frac{2 \sin{\left (x \right )} \cos{\left (x \right )}}{\left(\cos^{2}{\left (x \right )} + 1\right)^{2}} \left(- 4 \sin{\left (x \right )} \cos{\left (x \right )} + 1\right) - \frac{- 4 \sin^{2}{\left (x \right )} + 4 \cos^{2}{\left (x \right )}}{\cos^{2}{\left (x \right )} + 1}$$