Дано
$$25 left(20 sin^{2}{left (5 x right )} – 10 cos^{2}{left (5 x right )} – left(10 cos{left (5 x right )} + 11right) cos{left (5 x right )}right)$$
Подстановка условия
$$25 left(20 sin^{2}{left (5 x right )} – 10 cos^{2}{left (5 x right )} – left(10 cos{left (5 x right )} + 11right) cos{left (5 x right )}right)$$
25*(-10*cos(5*(1))^2 + 20*sin(5*(1))^2 – (11 + 10*cos(5*(1)))*cos(5*(1)))
$$25 left(20 sin^{2}{left (5 (1) right )} – 10 cos^{2}{left (5 (1) right )} – left(10 cos{left (5 (1) right )} + 11right) cos{left (5 (1) right )}right)$$
25*(-10*cos(5)^2 + 20*sin(5)^2 – (11 + 10*cos(5))*cos(5))
$$25 left(- left(10 cos{left (5 right )} + 11right) cos{left (5 right )} + – 10 cos^{2}{left (5 right )} + 20 sin^{2}{left (5 right )}right)$$
-250*cos(5)^2 + 500*sin(5)^2 – 25*(11 + 10*cos(5))*cos(5)
$$- 25 left(10 cos{left (5 right )} + 11right) cos{left (5 right )} – 250 cos^{2}{left (5 right )} + 500 sin^{2}{left (5 right )}$$
Степени
$$- 25 left(10 cos{left (5 x right )} + 11right) cos{left (5 x right )} + 500 sin^{2}{left (5 x right )} – 250 cos^{2}{left (5 x right )}$$
Численный ответ
500.0*sin(5*x)^2 – 250.0*cos(5*x)^2 – 25.0*(11.0 + 10.0*cos(5*x))*cos(5*x)
Рациональный знаменатель
$$- 25 left(10 cos{left (5 x right )} + 11right) cos{left (5 x right )} + 500 sin^{2}{left (5 x right )} – 250 cos^{2}{left (5 x right )}$$
Объединение рациональных выражений
$$- 25 left(10 cos{left (5 x right )} + 11right) cos{left (5 x right )} + 500 sin^{2}{left (5 x right )} – 250 cos^{2}{left (5 x right )}$$
Общее упрощение
-500*cos(10*x) – 275*cos(5*x)
$$- 275 cos{left (5 x right )} – 500 cos{left (10 x right )}$$
Соберем выражение
$$- 25 left(10 cos{left (5 x right )} + 11right) cos{left (5 x right )} + 500 sin^{2}{left (5 x right )} – 250 cos^{2}{left (5 x right )}$$
-500*cos(10*x) – 275*cos(5*x)
$$- 275 cos{left (5 x right )} – 500 cos{left (10 x right )}$$
Общий знаменатель
2 2
– 500*cos (5*x) – 275*cos(5*x) + 500*sin (5*x)
$$500 sin^{2}{left (5 x right )} – 500 cos^{2}{left (5 x right )} – 275 cos{left (5 x right )}$$
Тригонометрическая часть
-500*cos(10*x) – 275*cos(5*x)
$$- 275 cos{left (5 x right )} – 500 cos{left (10 x right )}$$
Комбинаторика
/ 2 2
-25* – 20*sin (5*x) + 11*cos(5*x) + 20*cos (5*x)/
$$- 25 left(- 20 sin^{2}{left (5 x right )} + 20 cos^{2}{left (5 x right )} + 11 cos{left (5 x right )}right)$$
Раскрыть выражение
2 2
/ 5 3 2 4 / 5 2 3 4 / 5 3 2 4 / 5 4 3 2
– 250*cos (x) – 10*cos (x)*sin (x) + 5*sin (x)*cos(x)/ + 500*sin (x) – 10*cos (x)*sin (x) + 5*cos (x)*sin(x)/ + 25*cos (x) – 10*cos (x)*sin (x) + 5*sin (x)*cos(x)/* -11 – 10*cos (x) – 50*sin (x)*cos(x) + 100*cos (x)*sin (x)/
$$- 250 left(5 sin^{4}{left (x right )} cos{left (x right )} – 10 sin^{2}{left (x right )} cos^{3}{left (x right )} + cos^{5}{left (x right )}right)^{2} + 25 left(5 sin^{4}{left (x right )} cos{left (x right )} – 10 sin^{2}{left (x right )} cos^{3}{left (x right )} + cos^{5}{left (x right )}right) left(- 50 sin^{4}{left (x right )} cos{left (x right )} + 100 sin^{2}{left (x right )} cos^{3}{left (x right )} – 10 cos^{5}{left (x right )} – 11right) + 500 left(sin^{5}{left (x right )} – 10 sin^{3}{left (x right )} cos^{2}{left (x right )} + 5 sin{left (x right )} cos^{4}{left (x right )}right)^{2}$$
