Общий знаменатель (sin(-a)/sin(180-a))-(tan ... ot(a))+(cos(a)/sin(90-a))

Вы ввели

  sin(-a)      tan(90 - a)      cos(a)  
------------ - ----------- + -----------
sin(180 - a)      cot(a)     sin(90 - a)

$$\frac{\sin{\left (- a \right )}}{\sin{\left (- a + 180 \right )}} - \frac{\tan{\left (- a + 90 \right )}}{\cot{\left (a \right )}} + \frac{\cos{\left (a \right )}}{\sin{\left (- a + 90 \right )}}$$

Степени

tan(-90 + a)       sin(a)         cos(a)   
------------ + ------------- - ------------
   cot(a)      sin(-180 + a)   sin(-90 + a)

$$\frac{\sin{\left (a \right )}}{\sin{\left (a - 180 \right )}} + \frac{\tan{\left (a - 90 \right )}}{\cot{\left (a \right )}} - \frac{\cos{\left (a \right )}}{\sin{\left (a - 90 \right )}}$$

Численный ответ

cos(a)/sin(90 - a) + sin(-a)/sin(180 - a) - tan(90 - a)/cot(a)

Рациональный знаменатель

cot(a)*sin(a)*sin(-90 + a) + sin(-180 + a)*sin(-90 + a)*tan(-90 + a) - cos(a)*cot(a)*sin(-180 + a)
--------------------------------------------------------------------------------------------------
                                cot(a)*sin(-180 + a)*sin(-90 + a)                                 

$$\frac{1}{\sin{\left (a - 180 \right )} \sin{\left (a - 90 \right )} \cot{\left (a \right )}} \left(\sin{\left (a \right )} \sin{\left (a - 90 \right )} \cot{\left (a \right )} + \sin{\left (a - 180 \right )} \sin{\left (a - 90 \right )} \tan{\left (a - 90 \right )} - \sin{\left (a - 180 \right )} \cos{\left (a \right )} \cot{\left (a \right )}\right)$$

Объединение рациональных выражений

(cot(a)*sin(a) + sin(-180 + a)*tan(-90 + a))*sin(-90 + a) - cos(a)*cot(a)*sin(-180 + a)
---------------------------------------------------------------------------------------
                           cot(a)*sin(-180 + a)*sin(-90 + a)                           

$$\frac{1}{\sin{\left (a - 180 \right )} \sin{\left (a - 90 \right )} \cot{\left (a \right )}} \left(\left(\sin{\left (a \right )} \cot{\left (a \right )} + \sin{\left (a - 180 \right )} \tan{\left (a - 90 \right )}\right) \sin{\left (a - 90 \right )} - \sin{\left (a - 180 \right )} \cos{\left (a \right )} \cot{\left (a \right )}\right)$$

Общее упрощение

    sin(a)                               cos(a)   
------------- + tan(a)*tan(-90 + a) - ------------
sin(-180 + a)                         sin(-90 + a)

$$\frac{\sin{\left (a \right )}}{\sin{\left (a - 180 \right )}} + \tan{\left (a \right )} \tan{\left (a - 90 \right )} - \frac{\cos{\left (a \right )}}{\sin{\left (a - 90 \right )}}$$

Собрать выражение

csc(-180 + a)*sin(a) + tan(a)*tan(-90 + a) - cos(a)*csc(-90 + a)

$$\sin{\left (a \right )} \csc{\left (a - 180 \right )} - \cos{\left (a \right )} \csc{\left (a - 90 \right )} + \tan{\left (a \right )} \tan{\left (a - 90 \right )}$$

Общий знаменатель

cos(a)*cot(a)*sin(180 - a) + cot(a)*sin(-a)*sin(90 - a) - sin(90 - a)*sin(180 - a)*tan(90 - a)
----------------------------------------------------------------------------------------------
                               cot(a)*sin(90 - a)*sin(180 - a)                                

$$\frac{1}{\sin{\left (- a + 90 \right )} \sin{\left (- a + 180 \right )} \cot{\left (a \right )}} \left(\sin{\left (- a \right )} \sin{\left (- a + 90 \right )} \cot{\left (a \right )} - \sin{\left (- a + 90 \right )} \sin{\left (- a + 180 \right )} \tan{\left (- a + 90 \right )} + \sin{\left (- a + 180 \right )} \cos{\left (a \right )} \cot{\left (a \right )}\right)$$

Тригонометрическая часть

    sin(a)         cos(a)                       
------------- + ----------- - tan(a)*tan(90 - a)
sin(-180 + a)   sin(90 - a)                     

$$\frac{\sin{\left (a \right )}}{\sin{\left (a - 180 \right )}} - \tan{\left (a \right )} \tan{\left (- a + 90 \right )} + \frac{\cos{\left (a \right )}}{\sin{\left (- a + 90 \right )}}$$

Комбинаторика

-(cos(a)*cot(a)*sin(-180 + a) - cot(a)*sin(a)*sin(-90 + a) - sin(-180 + a)*sin(-90 + a)*tan(-90 + a)) 
------------------------------------------------------------------------------------------------------
                                  cot(a)*sin(-180 + a)*sin(-90 + a)                                   

$$- \frac{1}{\sin{\left (a - 180 \right )} \sin{\left (a - 90 \right )} \cot{\left (a \right )}} \left(- \sin{\left (a \right )} \sin{\left (a - 90 \right )} \cot{\left (a \right )} - \sin{\left (a - 180 \right )} \sin{\left (a - 90 \right )} \tan{\left (a - 90 \right )} + \sin{\left (a - 180 \right )} \cos{\left (a \right )} \cot{\left (a \right )}\right)$$

Раскрыть выражение

              sin(a)                             cos(a)                    -tan(90) + tan(a)     
--------------------------------- - ------------------------------- + ---------------------------
cos(180)*sin(a) - cos(a)*sin(180)   cos(90)*sin(a) - cos(a)*sin(90)   (1 + tan(90)*tan(a))*cot(a)

$$\frac{\tan{\left (a \right )} - \tan{\left (90 \right )}}{\left(\tan{\left (90 \right )} \tan{\left (a \right )} + 1\right) \cot{\left (a \right )}} + \frac{\sin{\left (a \right )}}{\sin{\left (a \right )} \cos{\left (180 \right )} - \sin{\left (180 \right )} \cos{\left (a \right )}} - \frac{\cos{\left (a \right )}}{\sin{\left (a \right )} \cos{\left (90 \right )} - \sin{\left (90 \right )} \cos{\left (a \right )}}$$