Дано
$$- 2 sin{left (3 x right )} cos{left (3 x right )} cos{left (6 x right )} + 2 sin^{2}{left (3 x right )} sin{left (6 x right )}$$
Подстановка условия
$$- 2 sin{left (3 x right )} cos{left (3 x right )} cos{left (6 x right )} + 2 sin^{2}{left (3 x right )} sin{left (6 x right )}$$
(2*sin(3*(-3/2))^2)*sin(6*(-3/2)) – (2*cos(3*(-3/2)))*cos(6*(-3/2))*sin(3*(-3/2))
$$- 2 sin{left (3 (-3/2) right )} cos{left (3 (-3/2) right )} cos{left (6 (-3/2) right )} + 2 sin^{2}{left (3 (-3/2) right )} sin{left (6 (-3/2) right )}$$
(2*sin(3*(-3)/2)^2)*sin(6*(-3)/2) – (2*cos(3*(-3)/2))*cos(6*(-3)/2)*sin(3*(-3)/2)
$$2 sin^{2}{left (frac{-9}{2} right )} sin{left (frac{-18}{2} right )} – 2 sin{left (frac{-9}{2} right )} cos{left (frac{-9}{2} right )} cos{left (frac{-18}{2} right )}$$
-2*sin(9/2)^2*sin(9) + 2*cos(9)*cos(9/2)*sin(9/2)
$$- 2 sin^{2}{left (frac{9}{2} right )} sin{left (9 right )} + 2 sin{left (frac{9}{2} right )} cos{left (frac{9}{2} right )} cos{left (9 right )}$$
Степени
$$2 sin^{2}{left (3 x right )} sin{left (6 x right )} – 2 sin{left (3 x right )} cos{left (3 x right )} cos{left (6 x right )}$$
Численный ответ
2.0*sin(3*x)^2*sin(6*x) – 2.0*cos(3*x)*cos(6*x)*sin(3*x)
Рациональный знаменатель
$$2 sin^{2}{left (3 x right )} sin{left (6 x right )} – 2 sin{left (3 x right )} cos{left (3 x right )} cos{left (6 x right )}$$
Объединение рациональных выражений
$$2 left(sin{left (3 x right )} sin{left (6 x right )} – cos{left (3 x right )} cos{left (6 x right )}right) sin{left (3 x right )}$$
Общее упрощение
$$- 2 sin{left (3 x right )} cos{left (9 x right )}$$
Соберем выражение
$$sin{left (6 x right )} – sin{left (12 x right )}$$
Общий знаменатель
2
2*sin (3*x)*sin(6*x) – 2*cos(3*x)*cos(6*x)*sin(3*x)
$$2 sin^{2}{left (3 x right )} sin{left (6 x right )} – 2 sin{left (3 x right )} cos{left (3 x right )} cos{left (6 x right )}$$
Тригонометрическая часть
$$sin{left (6 x right )} – sin{left (12 x right )}$$
Комбинаторика
-2*(cos(3*x)*cos(6*x) – sin(3*x)*sin(6*x))*sin(3*x)
$$- 2 left(- sin{left (3 x right )} sin{left (6 x right )} + cos{left (3 x right )} cos{left (6 x right )}right) sin{left (3 x right )}$$
Раскрыть выражение
2
/ 3 2 / 3 3 5 5 / 3 2 / 3 2 / 6 6 4 2 2 4
2* – sin (x) + 3*cos (x)*sin(x)/ * – 20*cos (x)*sin (x) + 6*cos (x)*sin(x) + 6*sin (x)*cos(x)/ – – sin (x) + 3*cos (x)*sin(x)/*2*cos (x) – 6*sin (x)*cos(x)/*cos (x) – sin (x) – 15*cos (x)*sin (x) + 15*cos (x)*sin (x)/
$$- left(- 6 sin^{2}{left (x right )} cos{left (x right )} + 2 cos^{3}{left (x right )}right) left(- sin^{3}{left (x right )} + 3 sin{left (x right )} cos^{2}{left (x right )}right) left(- sin^{6}{left (x right )} + 15 sin^{4}{left (x right )} cos^{2}{left (x right )} – 15 sin^{2}{left (x right )} cos^{4}{left (x right )} + cos^{6}{left (x right )}right) + 2 left(- sin^{3}{left (x right )} + 3 sin{left (x right )} cos^{2}{left (x right )}right)^{2} left(6 sin^{5}{left (x right )} cos{left (x right )} – 20 sin^{3}{left (x right )} cos^{3}{left (x right )} + 6 sin{left (x right )} cos^{5}{left (x right )}right)$$
