Дано
$$sin{left (2 x right )} – frac{sin{left (4 x right )}}{cos{left (x right )}} + left(cos{left (4 x right )} + 1right) cos{left (5 x right )}$$
Подстановка условия
$$sin{left (2 x right )} – frac{sin{left (4 x right )}}{cos{left (x right )}} + left(cos{left (4 x right )} + 1right) cos{left (5 x right )}$$
sin(2*(1)) – sin(4*(1))/cos((1)) + cos(5*(1))*(1 + cos(4*(1)))
$$sin{left (2 (1) right )} – frac{sin{left (4 (1) right )}}{cos{left ((1) right )}} + left(cos{left (4 (1) right )} + 1right) cos{left (5 (1) right )}$$
sin(2) – sin(4)/cos(1) + cos(5)*(1 + cos(4))
$$left(cos{left (4 right )} + 1right) cos{left (5 right )} + sin{left (2 right )} – frac{sin{left (4 right )}}{cos{left (1 right )}}$$
(1 + cos(4))*cos(5) – sin(4)/cos(1) + sin(2)
$$left(cos{left (4 right )} + 1right) cos{left (5 right )} + sin{left (2 right )} – frac{sin{left (4 right )}}{cos{left (1 right )}}$$
Степени
$$left(cos{left (4 x right )} + 1right) cos{left (5 x right )} + sin{left (2 x right )} – frac{sin{left (4 x right )}}{cos{left (x right )}}$$
Численный ответ
(1.0 + cos(4*x))*cos(5*x) – sin(4*x)/cos(x) + sin(2*x)
Рациональный знаменатель
$$frac{1}{cos{left (x right )}} left(left(cos{left (4 x right )} + 1right) cos{left (x right )} cos{left (5 x right )} + sin{left (2 x right )} cos{left (x right )} – sin{left (4 x right )}right)$$
Объединение рациональных выражений
$$frac{1}{cos{left (x right )}} left(left(cos{left (4 x right )} + 1right) cos{left (x right )} cos{left (5 x right )} + sin{left (2 x right )} cos{left (x right )} – sin{left (4 x right )}right)$$
Общее упрощение
-sin(4*x) + ((1 + cos(4*x))*cos(5*x) + sin(2*x))*cos(x)
——————————————————-
cos(x)
$$frac{1}{cos{left (x right )}} left(left(left(cos{left (4 x right )} + 1right) cos{left (5 x right )} + sin{left (2 x right )}right) cos{left (x right )} – sin{left (4 x right )}right)$$
Соберем выражение
$$left(cos{left (4 x right )} + 1right) cos{left (5 x right )} + sin{left (2 x right )} – frac{sin{left (4 x right )}}{cos{left (x right )}}$$
cos(x) cos(9*x)
—— + ——– – sec(x)*sin(4*x) + cos(5*x) + sin(2*x)
2 2
$$sin{left (2 x right )} – sin{left (4 x right )} sec{left (x right )} + frac{1}{2} cos{left (x right )} + cos{left (5 x right )} + frac{1}{2} cos{left (9 x right )}$$
Общий знаменатель
sin(4*x)
cos(4*x)*cos(5*x) – ——– + cos(5*x) + sin(2*x)
cos(x)
$$sin{left (2 x right )} – frac{sin{left (4 x right )}}{cos{left (x right )}} + cos{left (4 x right )} cos{left (5 x right )} + cos{left (5 x right )}$$
Тригонометрическая часть
sin(4*x)
(1 + cos(4*x))*cos(5*x) – ——– + sin(2*x)
cos(x)
$$left(cos{left (4 x right )} + 1right) cos{left (5 x right )} + sin{left (2 x right )} – frac{sin{left (4 x right )}}{cos{left (x right )}}$$
Комбинаторика
-sin(4*x) + cos(x)*cos(5*x) + cos(x)*sin(2*x) + cos(x)*cos(4*x)*cos(5*x)
————————————————————————
cos(x)
$$frac{1}{cos{left (x right )}} left(sin{left (2 x right )} cos{left (x right )} – sin{left (4 x right )} + cos{left (x right )} cos{left (4 x right )} cos{left (5 x right )} + cos{left (x right )} cos{left (5 x right )}right)$$
Раскрыть выражение
3 3
/ 5 3 2 4 / 4 4 2 2 – 4*sin (x)*cos(x) + 4*cos (x)*sin(x)
cos (x) – 10*cos (x)*sin (x) + 5*sin (x)*cos(x)/*1 + cos (x) + sin (x) – 6*cos (x)*sin (x)/ – ————————————- + 2*cos(x)*sin(x)
cos(x)
$$- frac{1}{cos{left (x right )}} left(- 4 sin^{3}{left (x right )} cos{left (x right )} + 4 sin{left (x right )} cos^{3}{left (x right )}right) + left(5 sin^{4}{left (x right )} cos{left (x right )} – 10 sin^{2}{left (x right )} cos^{3}{left (x right )} + cos^{5}{left (x right )}right) left(sin^{4}{left (x right )} – 6 sin^{2}{left (x right )} cos^{2}{left (x right )} + cos^{4}{left (x right )} + 1right) + 2 sin{left (x right )} cos{left (x right )}$$
