Дано
$$left(2 sin{left (3 a right )} – 3 cos{left (3 a right )}right)^{2} + 2 cos{left (3 a right )} + 3 sin{left (3 a right )}$$
Подстановка условия
$$left(2 sin{left (3 a right )} – 3 cos{left (3 a right )}right)^{2} + 2 cos{left (3 a right )} + 3 sin{left (3 a right )}$$
(2*sin(3*(-3/2)) – 3*cos(3*(-3/2)))^2 + 2*cos(3*(-3/2)) + 3*sin(3*(-3/2))
$$left(2 sin{left (3 (-3/2) right )} – 3 cos{left (3 (-3/2) right )}right)^{2} + 2 cos{left (3 (-3/2) right )} + 3 sin{left (3 (-3/2) right )}$$
(2*sin(3*(-3)/2) – 3*cos(3*(-3)/2))^2 + 2*cos(3*(-3)/2) + 3*sin(3*(-3)/2)
$$3 sin{left (frac{-9}{2} right )} + 2 cos{left (frac{-9}{2} right )} + left(- 3 cos{left (frac{-9}{2} right )} + 2 sin{left (frac{-9}{2} right )}right)^{2}$$
(-3*cos(9/2) – 2*sin(9/2))^2 – 3*sin(9/2) + 2*cos(9/2)
$$2 cos{left (frac{9}{2} right )} – 3 sin{left (frac{9}{2} right )} + left(- 3 cos{left (frac{9}{2} right )} – 2 sin{left (frac{9}{2} right )}right)^{2}$$
Степени
$$left(2 sin{left (3 a right )} – 3 cos{left (3 a right )}right)^{2} + 3 sin{left (3 a right )} + 2 cos{left (3 a right )}$$
Численный ответ
(2.0*sin(3*a) – 3.0*cos(3*a))^2 + 2.0*cos(3*a) + 3.0*sin(3*a)
Рациональный знаменатель
$$left(2 sin{left (3 a right )} – 3 cos{left (3 a right )}right)^{2} + 3 sin{left (3 a right )} + 2 cos{left (3 a right )}$$
Объединение рациональных выражений
$$left(2 sin{left (3 a right )} – 3 cos{left (3 a right )}right)^{2} + 3 sin{left (3 a right )} + 2 cos{left (3 a right )}$$
Общее упрощение
2
(-3*cos(3*a) + 2*sin(3*a)) + 2*cos(3*a) + 3*sin(3*a)
$$left(2 sin{left (3 a right )} – 3 cos{left (3 a right )}right)^{2} + 3 sin{left (3 a right )} + 2 cos{left (3 a right )}$$
Соберем выражение
$$left(2 sin{left (3 a right )} – 3 cos{left (3 a right )}right)^{2} + 3 sin{left (3 a right )} + 2 cos{left (3 a right )}$$
2
(-3*cos(3*a) + 2*sin(3*a)) + 2*cos(3*a) + 3*sin(3*a)
$$left(2 sin{left (3 a right )} – 3 cos{left (3 a right )}right)^{2} + 3 sin{left (3 a right )} + 2 cos{left (3 a right )}$$
Общий знаменатель
2 2
2*cos(3*a) + 3*sin(3*a) + 4*sin (3*a) + 9*cos (3*a) – 12*cos(3*a)*sin(3*a)
$$4 sin^{2}{left (3 a right )} – 12 sin{left (3 a right )} cos{left (3 a right )} + 3 sin{left (3 a right )} + 9 cos^{2}{left (3 a right )} + 2 cos{left (3 a right )}$$
Тригонометрическая часть
2
(-3*cos(3*a) + 2*sin(3*a)) + 2*cos(3*a) + 3*sin(3*a)
$$left(2 sin{left (3 a right )} – 3 cos{left (3 a right )}right)^{2} + 3 sin{left (3 a right )} + 2 cos{left (3 a right )}$$
Комбинаторика
2 2
2*cos(3*a) + 3*sin(3*a) + 4*sin (3*a) + 9*cos (3*a) – 12*cos(3*a)*sin(3*a)
$$4 sin^{2}{left (3 a right )} – 12 sin{left (3 a right )} cos{left (3 a right )} + 3 sin{left (3 a right )} + 9 cos^{2}{left (3 a right )} + 2 cos{left (3 a right )}$$
Раскрыть выражение
2
/ 3 3 2 2 3 3 2 2
– 3*cos (a) – 2*sin (a) + 6*cos (a)*sin(a) + 9*sin (a)*cos(a)/ – 3*sin (a) + 2*cos (a) – 6*sin (a)*cos(a) + 9*cos (a)*sin(a)
$$left(- 2 sin^{3}{left (a right )} + 9 sin^{2}{left (a right )} cos{left (a right )} + 6 sin{left (a right )} cos^{2}{left (a right )} – 3 cos^{3}{left (a right )}right)^{2} – 3 sin^{3}{left (a right )} – 6 sin^{2}{left (a right )} cos{left (a right )} + 9 sin{left (a right )} cos^{2}{left (a right )} + 2 cos^{3}{left (a right )}$$
