Общий знаменатель sin(9*x)/36+sin(7*x)/28+sin(3*x)/12+sin(x)/4

Вы ввели

sin(9*x)   sin(7*x)   sin(3*x)   sin(x)
-------- + -------- + -------- + ------
   36         28         12        4   

$$\frac{1}{28} \sin{\left (7 x \right )} + \frac{1}{36} \sin{\left (9 x \right )} + \frac{1}{12} \sin{\left (3 x \right )} + \frac{1}{4} \sin{\left (x \right )}$$

Степени

sin(x)   sin(3*x)   sin(7*x)   sin(9*x)
------ + -------- + -------- + --------
  4         12         28         36   

$$\frac{1}{4} \sin{\left (x \right )} + \frac{1}{12} \sin{\left (3 x \right )} + \frac{1}{28} \sin{\left (7 x \right )} + \frac{1}{36} \sin{\left (9 x \right )}$$

Численный ответ

0.25*sin(x) + 0.0277777777777778*sin(9*x) + 0.0357142857142857*sin(7*x) + 0.0833333333333333*sin(3*x)

Рациональный знаменатель

sin(x)   sin(3*x)   sin(7*x)   sin(9*x)
------ + -------- + -------- + --------
  4         12         28         36   

$$\frac{1}{4} \sin{\left (x \right )} + \frac{1}{12} \sin{\left (3 x \right )} + \frac{1}{28} \sin{\left (7 x \right )} + \frac{1}{36} \sin{\left (9 x \right )}$$

Объединение рациональных выражений

7*sin(9*x) + 9*sin(7*x) + 21*sin(3*x) + 63*sin(x)
-------------------------------------------------
                       252                       

$$\frac{1}{252} \left(63 \sin{\left (x \right )} + 21 \sin{\left (3 x \right )} + 9 \sin{\left (7 x \right )} + 7 \sin{\left (9 x \right )}\right)$$

Общее упрощение

sin(x)   sin(3*x)   sin(7*x)   sin(9*x)
------ + -------- + -------- + --------
  4         12         28         36   

$$\frac{1}{4} \sin{\left (x \right )} + \frac{1}{12} \sin{\left (3 x \right )} + \frac{1}{28} \sin{\left (7 x \right )} + \frac{1}{36} \sin{\left (9 x \right )}$$

Собрать выражение

sin(x)   sin(3*x)   sin(7*x)   sin(9*x)
------ + -------- + -------- + --------
  4         12         28         36   

$$\frac{1}{4} \sin{\left (x \right )} + \frac{1}{12} \sin{\left (3 x \right )} + \frac{1}{28} \sin{\left (7 x \right )} + \frac{1}{36} \sin{\left (9 x \right )}$$

Общий знаменатель

sin(x)   sin(3*x)   sin(7*x)   sin(9*x)
------ + -------- + -------- + --------
  4         12         28         36   

$$\frac{1}{4} \sin{\left (x \right )} + \frac{1}{12} \sin{\left (3 x \right )} + \frac{1}{28} \sin{\left (7 x \right )} + \frac{1}{36} \sin{\left (9 x \right )}$$

Тригонометрическая часть

sin(x)   sin(3*x)   sin(7*x)   sin(9*x)
------ + -------- + -------- + --------
  4         12         28         36   

$$\frac{1}{4} \sin{\left (x \right )} + \frac{1}{12} \sin{\left (3 x \right )} + \frac{1}{28} \sin{\left (7 x \right )} + \frac{1}{36} \sin{\left (9 x \right )}$$

Комбинаторика

7*sin(9*x) + 9*sin(7*x) + 21*sin(3*x) + 63*sin(x)
-------------------------------------------------
                       252                       

$$\frac{1}{252} \left(63 \sin{\left (x \right )} + 21 \sin{\left (3 x \right )} + 9 \sin{\left (7 x \right )} + 7 \sin{\left (9 x \right )}\right)$$

Раскрыть выражение

     3         7                  9                             6       3           4       3         2                6                8                  2       5           4       5   
  sin (x)   sin (x)   sin(x)   sin (x)      2       7      7*cos (x)*sin (x)   5*cos (x)*sin (x)   cos (x)*sin(x)   cos (x)*sin(x)   cos (x)*sin(x)   3*cos (x)*sin (x)   7*cos (x)*sin (x)
- ------- - ------- + ------ + ------- - cos (x)*sin (x) - ----------------- - ----------------- + -------------- + -------------- + -------------- + ----------------- + -----------------
     12        28       4         36                               3                   4                 4                4                4                  4                   2        

$$\frac{1}{36} \sin^{9}{\left (x \right )} - \sin^{7}{\left (x \right )} \cos^{2}{\left (x \right )} - \frac{1}{28} \sin^{7}{\left (x \right )} + \frac{7}{2} \sin^{5}{\left (x \right )} \cos^{4}{\left (x \right )} + \frac{3}{4} \sin^{5}{\left (x \right )} \cos^{2}{\left (x \right )} - \frac{7}{3} \sin^{3}{\left (x \right )} \cos^{6}{\left (x \right )} - \frac{5}{4} \sin^{3}{\left (x \right )} \cos^{4}{\left (x \right )} - \frac{1}{12} \sin^{3}{\left (x \right )} + \frac{1}{4} \sin{\left (x \right )} \cos^{8}{\left (x \right )} + \frac{1}{4} \sin{\left (x \right )} \cos^{6}{\left (x \right )} + \frac{1}{4} \sin{\left (x \right )} \cos^{2}{\left (x \right )} + \frac{1}{4} \sin{\left (x \right )}$$