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