sin(2*x+3*y)*cos(x-3*y)+s ... *y)*cos(2*x+3*y) если y=4 (упростите выражение)

Вы ввели

sin(2*x + 3*y)*cos(x - 3*y) + sin(x - 3*y)*cos(2*x + 3*y)

$$\sin{\left (x - 3 y \right )} \cos{\left (2 x + 3 y \right )} + \sin{\left (2 x + 3 y \right )} \cos{\left (x - 3 y \right )}$$

Подстановка условия

sin(2*x + 3*y)*cos(x - 3*y) + sin(x - 3*y)*cos(2*x + 3*y) при y = 4

sin(2*x + 3*y)*cos(x - 3*y) + sin(x - 3*y)*cos(2*x + 3*y)

$$\sin{\left (x - 3 y \right )} \cos{\left (2 x + 3 y \right )} + \sin{\left (2 x + 3 y \right )} \cos{\left (x - 3 y \right )}$$

sin(2*x + 3*(4))*cos(x - 3*(4)) + sin(x - 3*(4))*cos(2*x + 3*(4))

$$\sin{\left (3 (4) + 2 x \right )} \cos{\left (- 3 (4) + x \right )} + \sin{\left (- 3 (4) + x \right )} \cos{\left (3 (4) + 2 x \right )}$$

sin(2*x + 3*4)*cos(x - 3*4) + sin(x - 3*4)*cos(2*x + 3*4)

$$\sin{\left (x - 12 \right )} \cos{\left (2 x + 3 \cdot 4 \right )} + \sin{\left (2 x + 3 \cdot 4 \right )} \cos{\left (x - 12 \right )}$$

cos(-12 + x)*sin(12 + 2*x) + cos(12 + 2*x)*sin(-12 + x)

$$\sin{\left (x - 12 \right )} \cos{\left (2 x + 12 \right )} + \sin{\left (2 x + 12 \right )} \cos{\left (x - 12 \right )}$$

Численный ответ

cos(x - 3*y)*sin(2*x + 3*y) + cos(2*x + 3*y)*sin(x - 3*y)

Общее упрощение

sin(3*x)

$$\sin{\left (3 x \right )}$$

Собрать выражение

sin(3*x)

$$\sin{\left (3 x \right )}$$

Тригонометрическая часть

sin(3*x)

$$\sin{\left (3 x \right )}$$

Раскрыть выражение

(cos(x)*cos(3*y) + sin(x)*sin(3*y))*(cos(2*x)*sin(3*y) + cos(3*y)*sin(2*x)) - (cos(x)*sin(3*y) - cos(3*y)*sin(x))*(cos(2*x)*cos(3*y) - sin(2*x)*sin(3*y))

$$\left(\sin{\left (x \right )} \sin{\left (3 y \right )} + \cos{\left (x \right )} \cos{\left (3 y \right )}\right) \left(\sin{\left (2 x \right )} \cos{\left (3 y \right )} + \sin{\left (3 y \right )} \cos{\left (2 x \right )}\right) - \left(- \sin{\left (x \right )} \cos{\left (3 y \right )} + \sin{\left (3 y \right )} \cos{\left (x \right )}\right) \left(- \sin{\left (2 x \right )} \sin{\left (3 y \right )} + \cos{\left (2 x \right )} \cos{\left (3 y \right )}\right)$$