Дано
$$sin{left (3 x right )} left(- sin{left (5 x right )}right) – cos{left (3 x right )} cos{left (5 x right )}$$
Подстановка условия
$$sin{left (3 x right )} left(- sin{left (5 x right )}right) – cos{left (3 x right )} cos{left (5 x right )}$$
(-sin(5*(-1)))*sin(3*(-1)) – cos(5*(-1))*cos(3*(-1))
$$sin{left (3 (-1) right )} left(- sin{left (5 (-1) right )}right) – cos{left (3 (-1) right )} cos{left (5 (-1) right )}$$
(-sin(5*(-1)))*sin(3*(-1)) – cos(5*(-1))*cos(3*(-1))
$$sin{left (-1 cdot 3 right )} left(- sin{left (-1 cdot 5 right )}right) – cos{left (-1 cdot 3 right )} cos{left (-1 cdot 5 right )}$$
-cos(3)*cos(5) – sin(3)*sin(5)
$$- sin{left (3 right )} sin{left (5 right )} – cos{left (3 right )} cos{left (5 right )}$$
Степени
$$- sin{left (3 x right )} sin{left (5 x right )} – cos{left (3 x right )} cos{left (5 x right )}$$
Численный ответ
-cos(3*x)*cos(5*x) – 1.0*sin(3*x)*sin(5*x)
Рациональный знаменатель
$$- sin{left (3 x right )} sin{left (5 x right )} – cos{left (3 x right )} cos{left (5 x right )}$$
Объединение рациональных выражений
$$- sin{left (3 x right )} sin{left (5 x right )} – cos{left (3 x right )} cos{left (5 x right )}$$
Общее упрощение
$$- cos{left (2 x right )}$$
Соберем выражение
$$- cos{left (2 x right )}$$
Общий знаменатель
-cos(3*x)*cos(5*x) – sin(3*x)*sin(5*x)
$$- sin{left (3 x right )} sin{left (5 x right )} – cos{left (3 x right )} cos{left (5 x right )}$$
Тригонометрическая часть
$$- cos{left (2 x right )}$$
Комбинаторика
-cos(3*x)*cos(5*x) – sin(3*x)*sin(5*x)
$$- sin{left (3 x right )} sin{left (5 x right )} – cos{left (3 x right )} cos{left (5 x right )}$$
Раскрыть выражение
/ 3 2 / 5 2 3 4 / 3 2 / 5 3 2 4
sin (x) – 3*cos (x)*sin(x)/*sin (x) – 10*cos (x)*sin (x) + 5*cos (x)*sin(x)/ – cos (x) – 3*sin (x)*cos(x)/*cos (x) – 10*cos (x)*sin (x) + 5*sin (x)*cos(x)/
$$- left(- 3 sin^{2}{left (x right )} cos{left (x right )} + cos^{3}{left (x right )}right) left(5 sin^{4}{left (x right )} cos{left (x right )} – 10 sin^{2}{left (x right )} cos^{3}{left (x right )} + cos^{5}{left (x right )}right) + left(sin^{3}{left (x right )} – 3 sin{left (x right )} cos^{2}{left (x right )}right) left(sin^{5}{left (x right )} – 10 sin^{3}{left (x right )} cos^{2}{left (x right )} + 5 sin{left (x right )} cos^{4}{left (x right )}right)$$