Дано
$$frac{sin{left (2 x right )} + sin{left (5 x right )} – sin{left (3 x right )}}{cos{left (x right )} + 1 – 2 sin^{2}{left (2 x right )}}$$
Подстановка условия
$$frac{sin{left (2 x right )} + sin{left (5 x right )} – sin{left (3 x right )}}{cos{left (x right )} + 1 – 2 sin^{2}{left (2 x right )}}$$
(sin(2*(2)) + sin(5*(2)) – sin(3*(2)))/(cos((2)) + 1 – 2*sin(2*(2))^2)
$$frac{sin{left (2 (2) right )} + sin{left (5 (2) right )} – sin{left (3 (2) right )}}{cos{left ((2) right )} + 1 – 2 sin^{2}{left (2 (2) right )}}$$
(sin(2*2) + sin(5*2) – sin(3*2))/(cos(2) + 1 – 2*sin(2*2)^2)
$$frac{sin{left (2 cdot 2 right )} + sin{left (2 cdot 5 right )} – sin{left (2 cdot 3 right )}}{- 2 sin^{2}{left (2 cdot 2 right )} + cos{left (2 right )} + 1}$$
(-sin(6) + sin(4) + sin(10))/(1 – 2*sin(4)^2 + cos(2))
$$frac{sin{left (4 right )} + sin{left (10 right )} – sin{left (6 right )}}{- 2 sin^{2}{left (4 right )} + cos{left (2 right )} + 1}$$
Степени
$$frac{sin{left (2 x right )} – sin{left (3 x right )} + sin{left (5 x right )}}{- 2 sin^{2}{left (2 x right )} + cos{left (x right )} + 1}$$
Численный ответ
(-sin(3*x) + sin(2*x) + sin(5*x))/(1.0 – 2.0*sin(2*x)^2 + cos(x))
Рациональный знаменатель
$$frac{sin{left (2 x right )} – sin{left (3 x right )} + sin{left (5 x right )}}{- 2 sin^{2}{left (2 x right )} + cos{left (x right )} + 1}$$
Объединение рациональных выражений
$$frac{sin{left (2 x right )} – sin{left (3 x right )} + sin{left (5 x right )}}{- 2 sin^{2}{left (2 x right )} + cos{left (x right )} + 1}$$
Общее упрощение
-sin(3*x) + sin(2*x) + sin(5*x)
——————————-
2
1 – 2*sin (2*x) + cos(x)
$$frac{sin{left (2 x right )} – sin{left (3 x right )} + sin{left (5 x right )}}{- 2 sin^{2}{left (2 x right )} + cos{left (x right )} + 1}$$
Соберем выражение
$$frac{sin{left (2 x right )} – sin{left (3 x right )} + sin{left (5 x right )}}{- 2 sin^{2}{left (2 x right )} + cos{left (x right )} + 1}$$
sin(2*x) sin(5*x) sin(3*x)
—————– + —————– – —————–
cos(x) + cos(4*x) cos(x) + cos(4*x) cos(x) + cos(4*x)
$$frac{sin{left (2 x right )}}{cos{left (x right )} + cos{left (4 x right )}} – frac{sin{left (3 x right )}}{cos{left (x right )} + cos{left (4 x right )}} + frac{sin{left (5 x right )}}{cos{left (x right )} + cos{left (4 x right )}}$$
Общий знаменатель
-sin(3*x) + sin(2*x) + sin(5*x)
——————————-
2
1 – 2*sin (2*x) + cos(x)
$$frac{sin{left (2 x right )} – sin{left (3 x right )} + sin{left (5 x right )}}{- 2 sin^{2}{left (2 x right )} + cos{left (x right )} + 1}$$
Тригонометрическая часть
-sin(3*x) + sin(2*x) + sin(5*x)
——————————-
cos(x) + cos(4*x)
$$frac{sin{left (2 x right )} – sin{left (3 x right )} + sin{left (5 x right )}}{cos{left (x right )} + cos{left (4 x right )}}$$
Комбинаторика
-sin(3*x) + sin(2*x) + sin(5*x)
——————————-
2
1 – 2*sin (2*x) + cos(x)
$$frac{sin{left (2 x right )} – sin{left (3 x right )} + sin{left (5 x right )}}{- 2 sin^{2}{left (2 x right )} + cos{left (x right )} + 1}$$
Раскрыть выражение
3 5 2 3 2 4
sin (x) + sin (x) – 10*cos (x)*sin (x) – 3*cos (x)*sin(x) + 2*cos(x)*sin(x) + 5*cos (x)*sin(x)
———————————————————————————————-
2 2
1 – 8*cos (x)*sin (x) + cos(x)
$$frac{1}{- 8 sin^{2}{left (x right )} cos^{2}{left (x right )} + cos{left (x right )} + 1} left(sin^{5}{left (x right )} – 10 sin^{3}{left (x right )} cos^{2}{left (x right )} + sin^{3}{left (x right )} + 5 sin{left (x right )} cos^{4}{left (x right )} – 3 sin{left (x right )} cos^{2}{left (x right )} + 2 sin{left (x right )} cos{left (x right )}right)$$
