cos(2*a)*cos(3*a)-sin(2*a)*sin(3*a) если a=3 (упростите выражение)

Вы ввели

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

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

Подстановка условия

cos(2*a)*cos(3*a) - sin(2*a)*sin(3*a) при a = 3

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

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

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

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

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

$$\cos{\left (2 \cdot 3 \right )} \cos{\left (3 \cdot 3 \right )} - \sin{\left (2 \cdot 3 \right )} \sin{\left (3 \cdot 3 \right )}$$

cos(6)*cos(9) - sin(6)*sin(9)

$$\cos{\left (6 \right )} \cos{\left (9 \right )} - \sin{\left (6 \right )} \sin{\left (9 \right )}$$

Численный ответ

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

Общее упрощение

cos(5*a)

$$\cos{\left (5 a \right )}$$

Собрать выражение

cos(5*a)

$$\cos{\left (5 a \right )}$$

Тригонометрическая часть

cos(5*a)

$$\cos{\left (5 a \right )}$$

Раскрыть выражение

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

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