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