Дано
$$sin{left (3 a right )} cos{left (a + frac{3 p}{2} right )} + cos{left (a right )} cos{left (- 3 a + 2 p right )}$$
Подстановка условия
$$sin{left (3 a right )} cos{left (a + frac{3 p}{2} right )} + cos{left (a right )} cos{left (- 3 a + 2 p right )}$$
cos(2*p – 3*(3/2))*cos((3/2)) + sin(3*(3/2))*cos((3*p)/2 + (3/2))
$$sin{left (3 (3/2) right )} cos{left ((3/2) + frac{3 p}{2} right )} + cos{left ((3/2) right )} cos{left (- 3 (3/2) + 2 p right )}$$
cos(2*p – 3*3/2)*cos(3/2) + sin(3*3/2)*cos((3*p)/2 + 3/2)
$$cos{left (frac{3}{2} right )} cos{left (2 p – frac{9}{2} right )} + sin{left (frac{9}{2} right )} cos{left (frac{3 p}{2} + frac{3}{2} right )}$$
cos(3/2)*cos(-9/2 + 2*p) + cos(3/2 + 3*p/2)*sin(9/2)
$$sin{left (frac{9}{2} right )} cos{left (frac{3 p}{2} + frac{3}{2} right )} + cos{left (frac{3}{2} right )} cos{left (2 p – frac{9}{2} right )}$$
Степени
$$sin{left (3 a right )} cos{left (a + frac{3 p}{2} right )} + cos{left (a right )} cos{left (3 a – 2 p right )}$$
Численный ответ
cos(a)*cos(2*p – 3*a) + cos((3*p)/2 + a)*sin(3*a)
Рациональный знаменатель
$$sin{left (3 a right )} cos{left (a + frac{3 p}{2} right )} + cos{left (a right )} cos{left (3 a – 2 p right )}$$
Объединение рациональных выражений
$$sin{left (3 a right )} cos{left (frac{1}{2} left(2 a + 3 pright) right )} + cos{left (a right )} cos{left (3 a – 2 p right )}$$
Общее упрощение
/ 3*p
cos(a)*cos(-2*p + 3*a) + cos|a + —|*sin(3*a)
2 /
$$sin{left (3 a right )} cos{left (a + frac{3 p}{2} right )} + cos{left (a right )} cos{left (3 a – 2 p right )}$$
Соберем выражение
$$frac{1}{2} sin{left (2 a – frac{3 p}{2} right )} + frac{1}{2} sin{left (4 a + frac{3 p}{2} right )} + frac{1}{2} cos{left (2 a – 2 p right )} + frac{1}{2} cos{left (4 a – 2 p right )}$$
Общий знаменатель
/ 3*p
cos(a)*cos(-2*p + 3*a) + cos|a + —|*sin(3*a)
2 /
$$sin{left (3 a right )} cos{left (a + frac{3 p}{2} right )} + cos{left (a right )} cos{left (3 a – 2 p right )}$$
Тригонометрическая часть
/ 3*p
cos(a)*cos(-2*p + 3*a) + cos|a + —|*sin(3*a)
2 /
$$sin{left (3 a right )} cos{left (a + frac{3 p}{2} right )} + cos{left (a right )} cos{left (3 a – 2 p right )}$$
Комбинаторика
/ 3*p
cos(a)*cos(-2*p + 3*a) + cos|a + —|*sin(3*a)
2 /
$$sin{left (3 a right )} cos{left (a + frac{3 p}{2} right )} + cos{left (a right )} cos{left (3 a – 2 p right )}$$
Раскрыть выражение
/ 3 2 / /3*p /3*p
– sin (a) + 3*cos (a)*sin(a)/*|cos(a)*cos|—| – sin(a)*sin|—|| + (cos(2*p)*cos(3*a) + sin(2*p)*sin(3*a))*cos(a)
2 / 2 //
$$left(- sin{left (a right )} sin{left (frac{3 p}{2} right )} + cos{left (a right )} cos{left (frac{3 p}{2} right )}right) left(- sin^{3}{left (a right )} + 3 sin{left (a right )} cos^{2}{left (a right )}right) + left(sin{left (3 a right )} sin{left (2 p right )} + cos{left (3 a right )} cos{left (2 p right )}right) cos{left (a right )}$$
