Дано
$$frac{sin{left (4 x right )} + sin{left (5 x right )} + sin{left (6 x right )}}{left(cos{left (4 x right )} + cos{left (5 x right )} + cos{left (6 x right )}right)^{1}}$$
Подстановка условия
$$frac{sin{left (4 x right )} + sin{left (5 x right )} + sin{left (6 x right )}}{left(cos{left (4 x right )} + cos{left (5 x right )} + cos{left (6 x right )}right)^{1}}$$
(sin(4*(-2)) + sin(5*(-2)) + sin(6*(-2)))/(cos(4*(-2)) + cos(5*(-2)) + cos(6*(-2)))^1
$$frac{sin{left (4 (-2) right )} + sin{left (5 (-2) right )} + sin{left (6 (-2) right )}}{left(cos{left (4 (-2) right )} + cos{left (5 (-2) right )} + cos{left (6 (-2) right )}right)^{1}}$$
(sin(4*(-2)) + sin(5*(-2)) + sin(6*(-2)))/(cos(4*(-2)) + cos(5*(-2)) + cos(6*(-2)))^1
$$frac{sin{left (-2 cdot 4 right )} + sin{left (-2 cdot 5 right )} + sin{left (-2 cdot 6 right )}}{left(cos{left (-2 cdot 5 right )} + cos{left (-2 cdot 4 right )} + cos{left (-2 cdot 6 right )}right)^{1}}$$
(-sin(8) – sin(10) – sin(12))/(cos(8) + cos(10) + cos(12))
$$frac{- sin{left (8 right )} – sin{left (12 right )} – sin{left (10 right )}}{cos{left (10 right )} + cos{left (8 right )} + cos{left (12 right )}}$$
Степени
$$frac{sin{left (4 x right )} + sin{left (5 x right )} + sin{left (6 x right )}}{cos{left (4 x right )} + cos{left (5 x right )} + cos{left (6 x right )}}$$
Численный ответ
(sin(4*x) + sin(5*x) + sin(6*x))/(cos(4*x) + cos(5*x) + cos(6*x))
Рациональный знаменатель
$$frac{sin{left (4 x right )} + sin{left (5 x right )} + sin{left (6 x right )}}{cos{left (4 x right )} + cos{left (5 x right )} + cos{left (6 x right )}}$$
Объединение рациональных выражений
$$frac{sin{left (4 x right )} + sin{left (5 x right )} + sin{left (6 x right )}}{cos{left (4 x right )} + cos{left (5 x right )} + cos{left (6 x right )}}$$
Общее упрощение
sin(4*x) + sin(5*x) + sin(6*x)
——————————
cos(4*x) + cos(5*x) + cos(6*x)
$$frac{sin{left (4 x right )} + sin{left (5 x right )} + sin{left (6 x right )}}{cos{left (4 x right )} + cos{left (5 x right )} + cos{left (6 x right )}}$$
Соберем выражение
$$frac{sin{left (4 x right )}}{cos{left (4 x right )} + cos{left (5 x right )} + cos{left (6 x right )}} + frac{sin{left (5 x right )}}{cos{left (4 x right )} + cos{left (5 x right )} + cos{left (6 x right )}} + frac{sin{left (6 x right )}}{cos{left (4 x right )} + cos{left (5 x right )} + cos{left (6 x right )}}$$
sin(4*x) + sin(5*x) + sin(6*x)
——————————
cos(4*x) + cos(5*x) + cos(6*x)
$$frac{sin{left (4 x right )} + sin{left (5 x right )} + sin{left (6 x right )}}{cos{left (4 x right )} + cos{left (5 x right )} + cos{left (6 x right )}}$$
Общий знаменатель
sin(4*x) + sin(5*x) + sin(6*x)
——————————
cos(4*x) + cos(5*x) + cos(6*x)
$$frac{sin{left (4 x right )} + sin{left (5 x right )} + sin{left (6 x right )}}{cos{left (4 x right )} + cos{left (5 x right )} + cos{left (6 x right )}}$$
Тригонометрическая часть
sin(4*x) + sin(5*x) + sin(6*x)
——————————
cos(4*x) + cos(5*x) + cos(6*x)
$$frac{sin{left (4 x right )} + sin{left (5 x right )} + sin{left (6 x right )}}{cos{left (4 x right )} + cos{left (5 x right )} + cos{left (6 x right )}}$$
Комбинаторика
sin(4*x) + sin(5*x) + sin(6*x)
——————————
cos(4*x) + cos(5*x) + cos(6*x)
$$frac{sin{left (4 x right )} + sin{left (5 x right )} + sin{left (6 x right )}}{cos{left (4 x right )} + cos{left (5 x right )} + cos{left (6 x right )}}$$
Раскрыть выражение
5 3 3 2 3 3 3 4 5 5
sin (x) – 20*cos (x)*sin (x) – 10*cos (x)*sin (x) – 4*sin (x)*cos(x) + 4*cos (x)*sin(x) + 5*cos (x)*sin(x) + 6*cos (x)*sin(x) + 6*sin (x)*cos(x)
—————————————————————————————————————————————————–
4 5 6 4 6 4 2 3 2 2 2 4 2 4
cos (x) + cos (x) + cos (x) + sin (x) – sin (x) – 15*cos (x)*sin (x) – 10*cos (x)*sin (x) – 6*cos (x)*sin (x) + 5*sin (x)*cos(x) + 15*cos (x)*sin (x)
$$frac{6 sin^{5}{left (x right )} cos{left (x right )} + sin^{5}{left (x right )} – 20 sin^{3}{left (x right )} cos^{3}{left (x right )} – 10 sin^{3}{left (x right )} cos^{2}{left (x right )} – 4 sin^{3}{left (x right )} cos{left (x right )} + 6 sin{left (x right )} cos^{5}{left (x right )} + 5 sin{left (x right )} cos^{4}{left (x right )} + 4 sin{left (x right )} cos^{3}{left (x right )}}{- sin^{6}{left (x right )} + 15 sin^{4}{left (x right )} cos^{2}{left (x right )} + 5 sin^{4}{left (x right )} cos{left (x right )} + sin^{4}{left (x right )} – 15 sin^{2}{left (x right )} cos^{4}{left (x right )} – 10 sin^{2}{left (x right )} cos^{3}{left (x right )} – 6 sin^{2}{left (x right )} cos^{2}{left (x right )} + cos^{6}{left (x right )} + cos^{5}{left (x right )} + cos^{4}{left (x right )}}$$
