Общий знаменатель (cos(a)-2*sin(a))/(sin(a) ... (2-cos(a)^(2))/(cos(2*a))

Вы ввели

                           2   
cos(a) - 2*sin(a)   2 - cos (a)
----------------- - -----------
 sin(a) + cos(a)      cos(2*a) 

$$\frac{- 2 \sin{\left (a \right )} + \cos{\left (a \right )}}{\sin{\left (a \right )} + \cos{\left (a \right )}} - \frac{- \cos^{2}{\left (a \right )} + 2}{\cos{\left (2 a \right )}}$$

Степени

                             2   
-2*sin(a) + cos(a)   -2 + cos (a)
------------------ + ------------
 cos(a) + sin(a)       cos(2*a)  

$$\frac{- 2 \sin{\left (a \right )} + \cos{\left (a \right )}}{\sin{\left (a \right )} + \cos{\left (a \right )}} + \frac{\cos^{2}{\left (a \right )} - 2}{\cos{\left (2 a \right )}}$$

Численный ответ

(-2.0*sin(a) + cos(a))/(cos(a) + sin(a)) - (2.0 - cos(a)^2)/cos(2*a)

Рациональный знаменатель

/        2   \                                                  
\-2 + cos (a)/*(cos(a) + sin(a)) + (-2*sin(a) + cos(a))*cos(2*a)
----------------------------------------------------------------
                   (cos(a) + sin(a))*cos(2*a)                   

$$\frac{1}{\left(\sin{\left (a \right )} + \cos{\left (a \right )}\right) \cos{\left (2 a \right )}} \left(\left(- 2 \sin{\left (a \right )} + \cos{\left (a \right )}\right) \cos{\left (2 a \right )} + \left(\sin{\left (a \right )} + \cos{\left (a \right )}\right) \left(\cos^{2}{\left (a \right )} - 2\right)\right)$$

Объединение рациональных выражений

                                /       2   \                  
(-2*sin(a) + cos(a))*cos(2*a) - \2 - cos (a)/*(cos(a) + sin(a))
---------------------------------------------------------------
                   (cos(a) + sin(a))*cos(2*a)                  

$$\frac{1}{\left(\sin{\left (a \right )} + \cos{\left (a \right )}\right) \cos{\left (2 a \right )}} \left(\left(- 2 \sin{\left (a \right )} + \cos{\left (a \right )}\right) \cos{\left (2 a \right )} - \left(\sin{\left (a \right )} + \cos{\left (a \right )}\right) \left(- \cos^{2}{\left (a \right )} + 2\right)\right)$$

Общее упрощение

     ___ /      ___    /    pi\       \       
-3*\/ 2 *|1 + \/ 2 *cos|a + --|*sin(a)|*sin(a)
         \             \    4 /       /       
----------------------------------------------
                          /    pi\            
            2*cos(2*a)*sin|a + --|            
                          \    4 /            

$$- \frac{3 \sqrt{2} \left(\sqrt{2} \sin{\left (a \right )} \cos{\left (a + \frac{\pi}{4} \right )} + 1\right) \sin{\left (a \right )}}{2 \sin{\left (a + \frac{\pi}{4} \right )} \cos{\left (2 a \right )}}$$

Собрать выражение

     cos(a)       /  3   cos(2*a)\                2*sin(a)   
--------------- + |- - + --------|*sec(2*a) - ---------------
cos(a) + sin(a)   \  2      2    /            cos(a) + sin(a)

$$\left(\frac{1}{2} \cos{\left (2 a \right )} - \frac{3}{2}\right) \sec{\left (2 a \right )} - \frac{2 \sin{\left (a \right )}}{\sin{\left (a \right )} + \cos{\left (a \right )}} + \frac{\cos{\left (a \right )}}{\sin{\left (a \right )} + \cos{\left (a \right )}}$$

Общий знаменатель

         3                               2                              
    - cos (a) + 2*cos(a) + 2*sin(a) - cos (a)*sin(a) + 3*cos(2*a)*sin(a)
1 - --------------------------------------------------------------------
                     cos(a)*cos(2*a) + cos(2*a)*sin(a)                  

$$1 - \frac{- \sin{\left (a \right )} \cos^{2}{\left (a \right )} + 3 \sin{\left (a \right )} \cos{\left (2 a \right )} + 2 \sin{\left (a \right )} - \cos^{3}{\left (a \right )} + 2 \cos{\left (a \right )}}{\sin{\left (a \right )} \cos{\left (2 a \right )} + \cos{\left (a \right )} \cos{\left (2 a \right )}}$$

Тригонометрическая часть

                   ___                     
1       3        \/ 2 *(-2*sin(a) + cos(a))
- - ---------- + --------------------------
2   2*cos(2*a)              /    pi\       
                       2*sin|a + --|       
                            \    4 /       

$$\frac{\sqrt{2} \left(- 2 \sin{\left (a \right )} + \cos{\left (a \right )}\right)}{2 \sin{\left (a + \frac{\pi}{4} \right )}} + \frac{1}{2} - \frac{3}{2 \cos{\left (2 a \right )}}$$

Комбинаторика

   3                               2                                                
cos (a) - 2*cos(a) - 2*sin(a) + cos (a)*sin(a) + cos(a)*cos(2*a) - 2*cos(2*a)*sin(a)
------------------------------------------------------------------------------------
                             (cos(a) + sin(a))*cos(2*a)                             

$$\frac{1}{\left(\sin{\left (a \right )} + \cos{\left (a \right )}\right) \cos{\left (2 a \right )}} \left(\sin{\left (a \right )} \cos^{2}{\left (a \right )} - 2 \sin{\left (a \right )} \cos{\left (2 a \right )} - 2 \sin{\left (a \right )} + \cos^{3}{\left (a \right )} + \cos{\left (a \right )} \cos{\left (2 a \right )} - 2 \cos{\left (a \right )}\right)$$

Раскрыть выражение

                               2      
-2*sin(a) + cos(a)      2 - cos (a)   
------------------ - -----------------
 cos(a) + sin(a)        2         2   
                     cos (a) - sin (a)

$$\frac{- 2 \sin{\left (a \right )} + \cos{\left (a \right )}}{\sin{\left (a \right )} + \cos{\left (a \right )}} - \frac{- \cos^{2}{\left (a \right )} + 2}{- \sin^{2}{\left (a \right )} + \cos^{2}{\left (a \right )}}$$