Дано
$$frac{sin^{2}{left (a right )} + 3 cos^{2}{left (a right )}}{cos^{2}{left (a right )} + 1 + cos^{4}{left (a right )}}$$
Подстановка условия
$$frac{sin^{2}{left (a right )} + 3 cos^{2}{left (a right )}}{cos^{2}{left (a right )} + 1 + cos^{4}{left (a right )}}$$
(3*cos((1/2))^2 + sin((1/2))^2)/(1 + cos((1/2))^2 + cos((1/2))^4)
$$frac{sin^{2}{left ((1/2) right )} + 3 cos^{2}{left ((1/2) right )}}{cos^{2}{left ((1/2) right )} + 1 + cos^{4}{left ((1/2) right )}}$$
(3*cos(1/2)^2 + sin(1/2)^2)/(1 + cos(1/2)^2 + cos(1/2)^4)
$$frac{sin^{2}{left (frac{1}{2} right )} + 3 cos^{2}{left (frac{1}{2} right )}}{cos^{4}{left (frac{1}{2} right )} + cos^{2}{left (frac{1}{2} right )} + 1}$$
(sin(1/2)^2 + 3*cos(1/2)^2)/(1 + cos(1/2)^2 + cos(1/2)^4)
$$frac{sin^{2}{left (frac{1}{2} right )} + 3 cos^{2}{left (frac{1}{2} right )}}{cos^{4}{left (frac{1}{2} right )} + cos^{2}{left (frac{1}{2} right )} + 1}$$
Степени
$$frac{sin^{2}{left (a right )} + 3 cos^{2}{left (a right )}}{cos^{4}{left (a right )} + cos^{2}{left (a right )} + 1}$$
Численный ответ
(sin(a)^2 + 3.0*cos(a)^2)/(1.0 + cos(a)^2 + cos(a)^4)
Рациональный знаменатель
$$frac{sin^{2}{left (a right )} + 3 cos^{2}{left (a right )}}{cos^{4}{left (a right )} + cos^{2}{left (a right )} + 1}$$
Объединение рациональных выражений
$$frac{sin^{2}{left (a right )} + 3 cos^{2}{left (a right )}}{cos^{4}{left (a right )} + cos^{2}{left (a right )} + 1}$$
Общее упрощение
2 + cos(2*a)
———————
2 4
1 + cos (a) + cos (a)
$$frac{cos{left (2 a right )} + 2}{cos^{4}{left (a right )} + cos^{2}{left (a right )} + 1}$$
Соберем выражение
$$frac{sin^{2}{left (a right )} + 3 cos^{2}{left (a right )}}{cos^{4}{left (a right )} + cos^{2}{left (a right )} + 1}$$
16 8*cos(2*a)
————————– + ————————–
15 + 8*cos(2*a) + cos(4*a) 15 + 8*cos(2*a) + cos(4*a)
$$frac{8 cos{left (2 a right )}}{8 cos{left (2 a right )} + cos{left (4 a right )} + 15} + frac{16}{8 cos{left (2 a right )} + cos{left (4 a right )} + 15}$$
Общий знаменатель
2 2
sin (a) + 3*cos (a)
———————
2 4
1 + cos (a) + cos (a)
$$frac{sin^{2}{left (a right )} + 3 cos^{2}{left (a right )}}{cos^{4}{left (a right )} + cos^{2}{left (a right )} + 1}$$
Тригонометрическая часть
2 + cos(2*a)
———————
2 4
1 + cos (a) + cos (a)
$$frac{cos{left (2 a right )} + 2}{cos^{2}{left (a right )} + 1 + cos^{4}{left (a right )}}$$
Комбинаторика
2 2
sin (a) + 3*cos (a)
———————————————
/ 2 / 2
1 + cos (a) – cos(a)/*1 + cos (a) + cos(a)/
$$frac{sin^{2}{left (a right )} + 3 cos^{2}{left (a right )}}{left(cos^{2}{left (a right )} – cos{left (a right )} + 1right) left(cos^{2}{left (a right )} + cos{left (a right )} + 1right)}$$
Раскрыть выражение
2 2
sin (a) + 3*cos (a)
———————
2 4
1 + cos (a) + cos (a)
$$frac{sin^{2}{left (a right )} + 3 cos^{2}{left (a right )}}{cos^{4}{left (a right )} + cos^{2}{left (a right )} + 1}$$
