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Общий знаменатель (4*cos(2*a)^(2)-4*cos(a)^ ... 2)-a)^(2)-sin(a-pi)^(22))

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Примеры

Решение

Вы ввели [src]
     2             2           2   
4*cos (2*a) - 4*cos (a) + 3*sin (a)
-----------------------------------
       2/5*pi    \      22         
  4*cos |---- - a| - sin  (a - pi) 
        \ 2      /
$$\frac{- 4 \cos^{2}{\left (a \right )} + 4 \cos^{2}{\left (2 a \right )} + 3 \sin^{2}{\left (a \right )}}{- \sin^{22}{\left (a - \pi \right )} + 4 \cos^{2}{\left (- a + \frac{5 \pi}{2} \right )}}$$
Степени [src]
       2           2           2     
- 4*cos (a) + 3*sin (a) + 4*cos (2*a)
-------------------------------------
             22           2          
        - sin  (a) + 4*sin (a)
$$\frac{3 \sin^{2}{\left (a \right )} - 4 \cos^{2}{\left (a \right )} + 4 \cos^{2}{\left (2 a \right )}}{- \sin^{22}{\left (a \right )} + 4 \sin^{2}{\left (a \right )}}$$
Численный ответ [src]
(4.0*cos(2*a)^2 + 3.0*sin(a)^2 - 4.0*cos(a)^2)/(-sin(a - pi)^22 + 4.0*cos((5*pi)/2 - a)^2)
Рациональный знаменатель [src]
       2           2           2     
- 4*cos (a) + 3*sin (a) + 4*cos (2*a)
-------------------------------------
       22                2/5*pi    \ 
  - sin  (a - pi) + 4*cos |---- - a| 
                          \ 2      /
$$\frac{3 \sin^{2}{\left (a \right )} - 4 \cos^{2}{\left (a \right )} + 4 \cos^{2}{\left (2 a \right )}}{- \sin^{22}{\left (a - \pi \right )} + 4 \cos^{2}{\left (- a + \frac{5 \pi}{2} \right )}}$$
Объединение рациональных выражений [src]
       2           2           2     
- 4*cos (a) + 3*sin (a) + 4*cos (2*a)
-------------------------------------
        22           2/-2*a + 5*pi\  
   - sin  (a) + 4*cos |-----------|  
                      \     2     /
$$\frac{3 \sin^{2}{\left (a \right )} - 4 \cos^{2}{\left (a \right )} + 4 \cos^{2}{\left (2 a \right )}}{- \sin^{22}{\left (a \right )} + 4 \cos^{2}{\left (\frac{1}{2} \left(- 2 a + 5 \pi\right) \right )}}$$
Общее упрощение [src]
          2   
9 - 16*sin (a)
--------------
        20    
-4 + sin  (a)
$$\frac{- 16 \sin^{2}{\left (a \right )} + 9}{\sin^{20}{\left (a \right )} - 4}$$
Собрать выражение [src]
                                                                                             3145728                                                                                                                                                                                         7340032*cos(2*a)                                                                                                                                                                                    4194304*cos(4*a)                                                                                        
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3841588 - 3547658*cos(2*a) - 497420*cos(4*a) - 170544*cos(8*a) - 26334*cos(12*a) - 1540*cos(16*a) - 22*cos(20*a) + 231*cos(18*a) + 7315*cos(14*a) + 74613*cos(10*a) + 319770*cos(6*a) + cos(22*a)   3841588 - 3547658*cos(2*a) - 497420*cos(4*a) - 170544*cos(8*a) - 26334*cos(12*a) - 1540*cos(16*a) - 22*cos(20*a) + 231*cos(18*a) + 7315*cos(14*a) + 74613*cos(10*a) + 319770*cos(6*a) + cos(22*a)   3841588 - 3547658*cos(2*a) - 497420*cos(4*a) - 170544*cos(8*a) - 26334*cos(12*a) - 1540*cos(16*a) - 22*cos(20*a) + 231*cos(18*a) + 7315*cos(14*a) + 74613*cos(10*a) + 319770*cos(6*a) + cos(22*a)
$$- \frac{7340032 \cos{\left (2 a \right )}}{- 3547658 \cos{\left (2 a \right )} - 497420 \cos{\left (4 a \right )} + 319770 \cos{\left (6 a \right )} - 170544 \cos{\left (8 a \right )} + 74613 \cos{\left (10 a \right )} - 26334 \cos{\left (12 a \right )} + 7315 \cos{\left (14 a \right )} - 1540 \cos{\left (16 a \right )} + 231 \cos{\left (18 a \right )} - 22 \cos{\left (20 a \right )} + \cos{\left (22 a \right )} + 3841588} + \frac{4194304 \cos{\left (4 a \right )}}{- 3547658 \cos{\left (2 a \right )} - 497420 \cos{\left (4 a \right )} + 319770 \cos{\left (6 a \right )} - 170544 \cos{\left (8 a \right )} + 74613 \cos{\left (10 a \right )} - 26334 \cos{\left (12 a \right )} + 7315 \cos{\left (14 a \right )} - 1540 \cos{\left (16 a \right )} + 231 \cos{\left (18 a \right )} - 22 \cos{\left (20 a \right )} + \cos{\left (22 a \right )} + 3841588} + \frac{3145728}{- 3547658 \cos{\left (2 a \right )} - 497420 \cos{\left (4 a \right )} + 319770 \cos{\left (6 a \right )} - 170544 \cos{\left (8 a \right )} + 74613 \cos{\left (10 a \right )} - 26334 \cos{\left (12 a \right )} + 7315 \cos{\left (14 a \right )} - 1540 \cos{\left (16 a \right )} + 231 \cos{\left (18 a \right )} - 22 \cos{\left (20 a \right )} + \cos{\left (22 a \right )} + 3841588}$$
     2           2             2   
3*sin (a) + 4*cos (2*a) - 4*cos (a)
-----------------------------------
      22                2/5*pi    \
 - sin  (a - pi) + 4*cos |---- - a|
                         \ 2      /
$$\frac{3 \sin^{2}{\left (a \right )} - 4 \cos^{2}{\left (a \right )} + 4 \cos^{2}{\left (2 a \right )}}{- \sin^{22}{\left (a - \pi \right )} + 4 \cos^{2}{\left (- a + \frac{5 \pi}{2} \right )}}$$
Комбинаторика [src]
 /       2           2           2     \ 
-\- 4*cos (a) + 3*sin (a) + 4*cos (2*a)/ 
-----------------------------------------
  /        10   \ /       10   \    2    
  \-2 + sin  (a)/*\2 + sin  (a)/*sin (a)
$$- \frac{3 \sin^{2}{\left (a \right )} - 4 \cos^{2}{\left (a \right )} + 4 \cos^{2}{\left (2 a \right )}}{\left(\sin^{10}{\left (a \right )} - 2\right) \left(\sin^{10}{\left (a \right )} + 2\right) \sin^{2}{\left (a \right )}}$$
Общий знаменатель [src]
 /       2           2           2     \ 
-\- 4*cos (a) + 3*sin (a) + 4*cos (2*a)/ 
-----------------------------------------
           22                2           
        sin  (a - pi) - 4*sin (a)
$$- \frac{3 \sin^{2}{\left (a \right )} - 4 \cos^{2}{\left (a \right )} + 4 \cos^{2}{\left (2 a \right )}}{- 4 \sin^{2}{\left (a \right )} + \sin^{22}{\left (a - \pi \right )}}$$
Тригонометрическая часть [src]
          2   
9 - 16*sin (a)
--------------
        20    
-4 + sin  (a)
$$\frac{- 16 \sin^{2}{\left (a \right )} + 9}{\sin^{20}{\left (a \right )} - 4}$$
Раскрыть выражение [src]
                                               2
       2           2        /   2         2   \ 
- 4*cos (a) + 3*sin (a) + 4*\cos (a) - sin (a)/ 
------------------------------------------------
                  22           2                
             - sin  (a) + 4*sin (a)
$$\frac{1}{- \sin^{22}{\left (a \right )} + 4 \sin^{2}{\left (a \right )}} \left(4 \left(- \sin^{2}{\left (a \right )} + \cos^{2}{\left (a \right )}\right)^{2} + 3 \sin^{2}{\left (a \right )} - 4 \cos^{2}{\left (a \right )}\right)$$