Дано
$$frac{3 sin^{2}{left (x right )} + cos^{4}{left (x right )}}{sin^{2}{left (x right )} + 1 + sin^{4}{left (x right )}}$$
Подстановка условия
$$frac{3 sin^{2}{left (x right )} + cos^{4}{left (x right )}}{sin^{2}{left (x right )} + 1 + sin^{4}{left (x right )}}$$
(3*sin((1))^2 + cos((1))^4)/(1 + sin((1))^2 + sin((1))^4)
$$frac{3 sin^{2}{left ((1) right )} + cos^{4}{left ((1) right )}}{sin^{2}{left ((1) right )} + 1 + sin^{4}{left ((1) right )}}$$
(3*sin(1)^2 + cos(1)^4)/(1 + sin(1)^2 + sin(1)^4)
$$frac{cos^{4}{left (1 right )} + 3 sin^{2}{left (1 right )}}{sin^{4}{left (1 right )} + sin^{2}{left (1 right )} + 1}$$
(cos(1)^4 + 3*sin(1)^2)/(1 + sin(1)^2 + sin(1)^4)
$$frac{cos^{4}{left (1 right )} + 3 sin^{2}{left (1 right )}}{sin^{4}{left (1 right )} + sin^{2}{left (1 right )} + 1}$$
Степени
$$frac{3 sin^{2}{left (x right )} + cos^{4}{left (x right )}}{sin^{4}{left (x right )} + sin^{2}{left (x right )} + 1}$$
Численный ответ
(cos(x)^4 + 3.0*sin(x)^2)/(1.0 + sin(x)^2 + sin(x)^4)
Рациональный знаменатель
$$frac{3 sin^{2}{left (x right )} + cos^{4}{left (x right )}}{sin^{4}{left (x right )} + sin^{2}{left (x right )} + 1}$$
Объединение рациональных выражений
$$frac{3 sin^{2}{left (x right )} + cos^{4}{left (x right )}}{sin^{4}{left (x right )} + sin^{2}{left (x right )} + 1}$$
Общее упрощение
$$1$$
Соберем выражение
$$frac{3 sin^{2}{left (x right )} + cos^{4}{left (x right )}}{sin^{4}{left (x right )} + sin^{2}{left (x right )} + 1}$$
$$1$$
Общий знаменатель
4 2
cos (x) + 3*sin (x)
———————
2 4
1 + sin (x) + sin (x)
$$frac{3 sin^{2}{left (x right )} + cos^{4}{left (x right )}}{sin^{4}{left (x right )} + sin^{2}{left (x right )} + 1}$$
Тригонометрическая часть
$$1$$
Комбинаторика
4 2
cos (x) + 3*sin (x)
———————————————
/ 2 / 2
1 + sin (x) – sin(x)/*1 + sin (x) + sin(x)/
$$frac{3 sin^{2}{left (x right )} + cos^{4}{left (x right )}}{left(sin^{2}{left (x right )} – sin{left (x right )} + 1right) left(sin^{2}{left (x right )} + sin{left (x right )} + 1right)}$$
Раскрыть выражение
4 2
cos (x) + 3*sin (x)
———————
2 4
1 + sin (x) + sin (x)
$$frac{3 sin^{2}{left (x right )} + cos^{4}{left (x right )}}{sin^{4}{left (x right )} + sin^{2}{left (x right )} + 1}$$
