Общий знаменатель (1-18*cos(x)^2/(-2+3*sin( ... x)))*cos(x)/(-2+3*sin(x))

Вы ввели

/             2                      \       
|       18*cos (x)         9*sin(x)  |       
|1 - ---------------- - -------------|*cos(x)
|                   2   -2 + 3*sin(x)|       
\    (-2 + 3*sin(x))                 /       
---------------------------------------------
                -2 + 3*sin(x)                

$$\frac{\cos{\left (x \right )}}{3 \sin{\left (x \right )} - 2} \left(1 - \frac{18 \cos^{2}{\left (x \right )}}{\left(3 \sin{\left (x \right )} - 2\right)^{2}} - \frac{9 \sin{\left (x \right )}}{3 \sin{\left (x \right )} - 2}\right)$$

Степени

/             2                      \       
|       18*cos (x)         9*sin(x)  |       
|1 - ---------------- - -------------|*cos(x)
|                   2   -2 + 3*sin(x)|       
\    (-2 + 3*sin(x))                 /       
---------------------------------------------
                -2 + 3*sin(x)                

$$\frac{\cos{\left (x \right )}}{3 \sin{\left (x \right )} - 2} \left(1 - \frac{9 \sin{\left (x \right )}}{3 \sin{\left (x \right )} - 2} - \frac{18 \cos^{2}{\left (x \right )}}{\left(3 \sin{\left (x \right )} - 2\right)^{2}}\right)$$

Численный ответ

(1.0 - 9.0*sin(x)/(-2.0 + 3.0*sin(x)) - 18.0*cos(x)^2/(-2.0 + 3.0*sin(x))^2)*cos(x)/(-2.0 + 3.0*sin(x))

Рациональный знаменатель

/                /               2         2   \                    2       \       
\(-2 + 3*sin(x))*\(-2 + 3*sin(x))  - 18*cos (x)/ - 9*(-2 + 3*sin(x)) *sin(x)/*cos(x)
------------------------------------------------------------------------------------
                                                 4                                  
                                  (-2 + 3*sin(x))                                   

$$\frac{\cos{\left (x \right )}}{\left(3 \sin{\left (x \right )} - 2\right)^{4}} \left(\left(\left(3 \sin{\left (x \right )} - 2\right)^{2} - 18 \cos^{2}{\left (x \right )}\right) \left(3 \sin{\left (x \right )} - 2\right) - 9 \left(3 \sin{\left (x \right )} - 2\right)^{2} \sin{\left (x \right )}\right)$$

Объединение рациональных выражений

/               2         2                              \       
\(-2 + 3*sin(x))  - 18*cos (x) - 9*(-2 + 3*sin(x))*sin(x)/*cos(x)
-----------------------------------------------------------------
                                        3                        
                         (-2 + 3*sin(x))                         

$$\frac{\cos{\left (x \right )}}{\left(3 \sin{\left (x \right )} - 2\right)^{3}} \left(\left(3 \sin{\left (x \right )} - 2\right)^{2} - 9 \left(3 \sin{\left (x \right )} - 2\right) \sin{\left (x \right )} - 18 \cos^{2}{\left (x \right )}\right)$$

Общее упрощение

(-14 + 6*sin(x))*cos(x)
-----------------------
                   3   
    (-2 + 3*sin(x))    

$$\frac{\left(6 \sin{\left (x \right )} - 14\right) \cos{\left (x \right )}}{\left(3 \sin{\left (x \right )} - 2\right)^{3}}$$

Собрать выражение

                            216*sin(2*x)                                                      36*cos(3*x)                                                        260*cos(x)                          
- --------------------------------------------------------------- - --------------------------------------------------------------- + ---------------------------------------------------------------
  1235 - 2064*sin(x) - 1188*cos(2*x) + 81*cos(4*x) + 432*sin(3*x)   1235 - 2064*sin(x) - 1188*cos(2*x) + 81*cos(4*x) + 432*sin(3*x)   1235 - 2064*sin(x) - 1188*cos(2*x) + 81*cos(4*x) + 432*sin(3*x)

$$- \frac{216 \sin{\left (2 x \right )}}{- 2064 \sin{\left (x \right )} + 432 \sin{\left (3 x \right )} - 1188 \cos{\left (2 x \right )} + 81 \cos{\left (4 x \right )} + 1235} + \frac{260 \cos{\left (x \right )}}{- 2064 \sin{\left (x \right )} + 432 \sin{\left (3 x \right )} - 1188 \cos{\left (2 x \right )} + 81 \cos{\left (4 x \right )} + 1235} - \frac{36 \cos{\left (3 x \right )}}{- 2064 \sin{\left (x \right )} + 432 \sin{\left (3 x \right )} - 1188 \cos{\left (2 x \right )} + 81 \cos{\left (4 x \right )} + 1235}$$

Комбинаторика

   /                     2           2   \       
-2*\-2 - 3*sin(x) + 9*cos (x) + 9*sin (x)/*cos(x)
-------------------------------------------------
                                3                
                 (-2 + 3*sin(x))                 

$$- \frac{2 \cos{\left (x \right )}}{\left(3 \sin{\left (x \right )} - 2\right)^{3}} \left(9 \sin^{2}{\left (x \right )} - 3 \sin{\left (x \right )} + 9 \cos^{2}{\left (x \right )} - 2\right)$$

Общий знаменатель

 /                  3                              2          \ 
-\-4*cos(x) + 18*cos (x) - 6*cos(x)*sin(x) + 18*sin (x)*cos(x)/ 
----------------------------------------------------------------
                       2            3                           
            -8 - 54*sin (x) + 27*sin (x) + 36*sin(x)            

$$- \frac{18 \sin^{2}{\left (x \right )} \cos{\left (x \right )} - 6 \sin{\left (x \right )} \cos{\left (x \right )} + 18 \cos^{3}{\left (x \right )} - 4 \cos{\left (x \right )}}{27 \sin^{3}{\left (x \right )} - 54 \sin^{2}{\left (x \right )} + 36 \sin{\left (x \right )} - 8}$$

Тригонометрическая часть

2*(-7 + 3*sin(x))*cos(x)
------------------------
                   3    
    (-2 + 3*sin(x))     

$$\frac{2 \left(3 \sin{\left (x \right )} - 7\right) \cos{\left (x \right )}}{\left(3 \sin{\left (x \right )} - 2\right)^{3}}$$

Раскрыть выражение

/             2                      \       
|       18*cos (x)         9*sin(x)  |       
|1 - ---------------- - -------------|*cos(x)
|                   2   -2 + 3*sin(x)|       
\    (-2 + 3*sin(x))                 /       
---------------------------------------------
                -2 + 3*sin(x)                

$$\frac{\cos{\left (x \right )}}{3 \sin{\left (x \right )} - 2} \left(1 - \frac{9 \sin{\left (x \right )}}{3 \sin{\left (x \right )} - 2} - \frac{18 \cos^{2}{\left (x \right )}}{\left(3 \sin{\left (x \right )} - 2\right)^{2}}\right)$$