(sin(a)+sin(5*a))/(cos(a)+cos(5*a)) если a=1 (упростите выражение)

Вы ввели

sin(a) + sin(5*a)
-----------------
cos(a) + cos(5*a)

$$\frac{\sin{\left (a \right )} + \sin{\left (5 a \right )}}{\cos{\left (a \right )} + \cos{\left (5 a \right )}}$$

Подстановка условия

(sin(a) + sin(5*a))/(cos(a) + cos(5*a)) при a = 1

(sin(a) + sin(5*a))/(cos(a) + cos(5*a))

$$\frac{\sin{\left (a \right )} + \sin{\left (5 a \right )}}{\cos{\left (a \right )} + \cos{\left (5 a \right )}}$$

(sin((1)) + sin(5*(1)))/(cos((1)) + cos(5*(1)))

$$\frac{\sin{\left ((1) \right )} + \sin{\left (5 (1) \right )}}{\cos{\left ((1) \right )} + \cos{\left (5 (1) \right )}}$$

(sin(1) + sin(5))/(cos(1) + cos(5))

$$\frac{\sin{\left (5 \right )} + \sin{\left (1 \right )}}{\cos{\left (5 \right )} + \cos{\left (1 \right )}}$$

(sin(1) + sin(5))/(cos(1) + cos(5))

$$\frac{\sin{\left (5 \right )} + \sin{\left (1 \right )}}{\cos{\left (5 \right )} + \cos{\left (1 \right )}}$$

Численный ответ

(sin(a) + sin(5*a))/(cos(a) + cos(5*a))

Собрать выражение

      sin(a)             sin(5*a)    
----------------- + -----------------
cos(a) + cos(5*a)   cos(a) + cos(5*a)

$$\frac{\sin{\left (a \right )}}{\cos{\left (a \right )} + \cos{\left (5 a \right )}} + \frac{\sin{\left (5 a \right )}}{\cos{\left (a \right )} + \cos{\left (5 a \right )}}$$

Раскрыть выражение

   5            2       3           4                   
sin (a) - 10*cos (a)*sin (a) + 5*cos (a)*sin(a) + sin(a)
--------------------------------------------------------
   5            3       2           4                   
cos (a) - 10*cos (a)*sin (a) + 5*sin (a)*cos(a) + cos(a)

$$\frac{\sin^{5}{\left (a \right )} - 10 \sin^{3}{\left (a \right )} \cos^{2}{\left (a \right )} + 5 \sin{\left (a \right )} \cos^{4}{\left (a \right )} + \sin{\left (a \right )}}{5 \sin^{4}{\left (a \right )} \cos{\left (a \right )} - 10 \sin^{2}{\left (a \right )} \cos^{3}{\left (a \right )} + \cos^{5}{\left (a \right )} + \cos{\left (a \right )}}$$