(sin(a)+sin(3*a))/((cos(a)+cos(3)*a)) если a=1/3 (упростите выражение)

Вы ввели

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

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

Подстановка условия

(sin(a) + sin(3*a))/(cos(a) + cos(3)*a)^1 при a = 1/3

(sin(a) + sin(3*a))/(cos(a) + cos(3)*a)^1

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

(sin((1/3)) + sin(3*(1/3)))/(cos((1/3)) + cos(3)*(1/3))^1

$$\frac{\sin{\left ((1/3) \right )} + \sin{\left (3 (1/3) \right )}}{\left((1/3) \cos{\left (3 \right )} + \cos{\left ((1/3) \right )}\right)^{1}}$$

(sin(1/3) + sin(3/3))/(cos(1/3) + cos(3)/3)^1

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

(sin(1) + sin(1/3))/(cos(3)/3 + cos(1/3))

$$\frac{\sin{\left (\frac{1}{3} \right )} + \sin{\left (1 \right )}}{\frac{1}{3} \cos{\left (3 \right )} + \cos{\left (\frac{1}{3} \right )}}$$

Степени

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

$$\frac{\sin{\left (a \right )} + \sin{\left (3 a \right )}}{a \cos{\left (3 \right )} + \cos{\left (a \right )}}$$

Численный ответ

(sin(a) + sin(3*a))/(-0.989992496600445*a + cos(a))

Рациональный знаменатель

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

$$\frac{\sin{\left (a \right )} + \sin{\left (3 a \right )}}{a \cos{\left (3 \right )} + \cos{\left (a \right )}}$$

Объединение рациональных выражений

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

$$\frac{\sin{\left (a \right )} + \sin{\left (3 a \right )}}{a \cos{\left (3 \right )} + \cos{\left (a \right )}}$$

Общее упрощение

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

$$\frac{\sin{\left (a \right )} + \sin{\left (3 a \right )}}{a \cos{\left (3 \right )} + \cos{\left (a \right )}}$$

Собрать выражение

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

$$\frac{\sin{\left (a \right )} + \sin{\left (3 a \right )}}{a \cos{\left (3 \right )} + \cos{\left (a \right )}}$$

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

$$\frac{\sin{\left (a \right )}}{a \cos{\left (3 \right )} + \cos{\left (a \right )}} + \frac{\sin{\left (3 a \right )}}{a \cos{\left (3 \right )} + \cos{\left (a \right )}}$$

Общий знаменатель

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

$$\frac{\sin{\left (a \right )} + \sin{\left (3 a \right )}}{a \cos{\left (3 \right )} + \cos{\left (a \right )}}$$

Комбинаторика

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

$$\frac{\sin{\left (a \right )} + \sin{\left (3 a \right )}}{a \cos{\left (3 \right )} + \cos{\left (a \right )}}$$

Тригонометрическая часть

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

$$\frac{\sin{\left (a \right )} + \sin{\left (3 a \right )}}{a \cos{\left (3 \right )} + \cos{\left (a \right )}}$$

Раскрыть выражение

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

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