Дано
$$- sin{left (5 x right )} sin{left (6 x right )} + – cos{left (5 x right )} cos{left (6 x right )}$$
Подстановка условия
$$- sin{left (5 x right )} sin{left (6 x right )} + – cos{left (5 x right )} cos{left (6 x right )}$$
(-cos(5*(-3/2)))*cos(6*(-3/2)) – sin(5*(-3/2))*sin(6*(-3/2))
$$- sin{left (5 (-3/2) right )} sin{left (6 (-3/2) right )} + – cos{left (5 (-3/2) right )} cos{left (6 (-3/2) right )}$$
(-cos(5*(-3)/2))*cos(6*(-3)/2) – sin(5*(-3)/2)*sin(6*(-3)/2)
$$- sin{left (frac{-15}{2} right )} sin{left (frac{-18}{2} right )} + – cos{left (frac{-15}{2} right )} cos{left (frac{-18}{2} right )}$$
-cos(9)*cos(15/2) – sin(9)*sin(15/2)
$$- sin{left (frac{15}{2} right )} sin{left (9 right )} – cos{left (frac{15}{2} right )} cos{left (9 right )}$$
Степени
$$- sin{left (5 x right )} sin{left (6 x right )} – cos{left (5 x right )} cos{left (6 x right )}$$
Численный ответ
-sin(5*x)*sin(6*x) – 1.0*cos(5*x)*cos(6*x)
Рациональный знаменатель
$$- sin{left (5 x right )} sin{left (6 x right )} – cos{left (5 x right )} cos{left (6 x right )}$$
Объединение рациональных выражений
$$- sin{left (5 x right )} sin{left (6 x right )} – cos{left (5 x right )} cos{left (6 x right )}$$
Общее упрощение
$$- cos{left (x right )}$$
Соберем выражение
$$- cos{left (x right )}$$
Общий знаменатель
-cos(5*x)*cos(6*x) – sin(5*x)*sin(6*x)
$$- sin{left (5 x right )} sin{left (6 x right )} – cos{left (5 x right )} cos{left (6 x right )}$$
Тригонометрическая часть
$$- cos{left (x right )}$$
Комбинаторика
-cos(5*x)*cos(6*x) – sin(5*x)*sin(6*x)
$$- sin{left (5 x right )} sin{left (6 x right )} – cos{left (5 x right )} cos{left (6 x right )}$$
Раскрыть выражение
/ 5 4 3 2 / 6 6 4 2 2 4 / 5 2 3 4 / 3 3 5 5
– cos (x) – 5*sin (x)*cos(x) + 10*cos (x)*sin (x)/*cos (x) – sin (x) – 15*cos (x)*sin (x) + 15*cos (x)*sin (x)/ – sin (x) – 10*cos (x)*sin (x) + 5*cos (x)*sin(x)/* – 20*cos (x)*sin (x) + 6*cos (x)*sin(x) + 6*sin (x)*cos(x)/
$$left(- 5 sin^{4}{left (x right )} cos{left (x right )} + 10 sin^{2}{left (x right )} cos^{3}{left (x right )} – cos^{5}{left (x right )}right) left(- sin^{6}{left (x right )} + 15 sin^{4}{left (x right )} cos^{2}{left (x right )} – 15 sin^{2}{left (x right )} cos^{4}{left (x right )} + cos^{6}{left (x right )}right) – left(6 sin^{5}{left (x right )} cos{left (x right )} – 20 sin^{3}{left (x right )} cos^{3}{left (x right )} + 6 sin{left (x right )} cos^{5}{left (x right )}right) left(sin^{5}{left (x right )} – 10 sin^{3}{left (x right )} cos^{2}{left (x right )} + 5 sin{left (x right )} cos^{4}{left (x right )}right)$$
