Общий знаменатель sin(pi-a)/sin(3*pi/2+a)+cos(pi-a)/cos(pi/2+a)-1

Вы ввели

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

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

Степени

     cos(a)   sin(a)
-1 + ------ - ------
     sin(a)   cos(a)

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

Численный ответ

-1.0 + cos(pi - a)/cos(pi/2 + a) + sin(pi - a)/sin((3*pi)/2 + a)

Рациональный знаменатель

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

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

Объединение рациональных выражений

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

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

Общее упрощение

                   2    
-1 - 2*tan(a) + --------
                sin(2*a)

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

Собрать выражение

     cos(a)   sin(a)
-1 + ------ - ------
     sin(a)   cos(a)

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

Комбинаторика

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

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

Общий знаменатель

     cos(a)*cos(pi - a) + sin(a)*sin(pi - a)
-1 - ---------------------------------------
                  cos(a)*sin(a)             

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

Тригонометрическая часть

       1            
-1 + ------ - tan(a)
     tan(a)         

$$- \tan{\left (a \right )} - 1 + \frac{1}{\tan{\left (a \right )}}$$

Раскрыть выражение

     cos(a)   sin(a)
-1 + ------ - ------
     sin(a)   cos(a)

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