Дано
$$frac{1}{sin^{2}{left (t right )}} left(sin^{4}{left (t right )} + cos^{4}{left (t right )}right) cos^{2}{left (t right )}$$
Подстановка условия
$$frac{1}{sin^{2}{left (t right )}} left(sin^{4}{left (t right )} + cos^{4}{left (t right )}right) cos^{2}{left (t right )}$$
((sin((1/2))^4 + cos((1/2))^4)/sin((1/2))^2)*cos((1/2))^2
$$frac{1}{sin^{2}{left ((1/2) right )}} left(sin^{4}{left ((1/2) right )} + cos^{4}{left ((1/2) right )}right) cos^{2}{left ((1/2) right )}$$
((sin(1/2)^4 + cos(1/2)^4)/sin(1/2)^2)*cos(1/2)^2
$$frac{1}{sin^{2}{left (frac{1}{2} right )}} left(sin^{4}{left (frac{1}{2} right )} + cos^{4}{left (frac{1}{2} right )}right) cos^{2}{left (frac{1}{2} right )}$$
cos(1/2)^2*(cos(1/2)^4 + sin(1/2)^4)/sin(1/2)^2
$$frac{cos^{2}{left (frac{1}{2} right )}}{sin^{2}{left (frac{1}{2} right )}} left(sin^{4}{left (frac{1}{2} right )} + cos^{4}{left (frac{1}{2} right )}right)$$
Степени
$$frac{cos^{2}{left (t right )}}{sin^{2}{left (t right )}} left(sin^{4}{left (t right )} + cos^{4}{left (t right )}right)$$
Численный ответ
cos(t)^2*(cos(t)^4 + sin(t)^4)/sin(t)^2
Рациональный знаменатель
$$frac{cos^{2}{left (t right )}}{sin^{2}{left (t right )}} left(sin^{4}{left (t right )} + cos^{4}{left (t right )}right)$$
Объединение рациональных выражений
$$frac{cos^{2}{left (t right )}}{sin^{2}{left (t right )}} left(sin^{4}{left (t right )} + cos^{4}{left (t right )}right)$$
Общее упрощение
4 4
cos (t) + sin (t)
—————–
2
tan (t)
$$frac{1}{tan^{2}{left (t right )}} left(sin^{4}{left (t right )} + cos^{4}{left (t right )}right)$$
Соберем выражение
$$left(frac{1}{4} cos{left (4 t right )} + frac{3}{4}right) cot^{2}{left (t right )}$$
2 / 4 4
cos (t)*cos (t) + sin (t)/
—————————
2
sin (t)
$$frac{cos^{2}{left (t right )}}{sin^{2}{left (t right )}} left(sin^{4}{left (t right )} + cos^{4}{left (t right )}right)$$
Комбинаторика
2 / 4 4
cos (t)*cos (t) + sin (t)/
—————————
2
sin (t)
$$frac{cos^{2}{left (t right )}}{sin^{2}{left (t right )}} left(sin^{4}{left (t right )} + cos^{4}{left (t right )}right)$$
Общий знаменатель
6
2 2 cos (t)
cos (t)*sin (t) + ——-
2
sin (t)
$$sin^{2}{left (t right )} cos^{2}{left (t right )} + frac{cos^{6}{left (t right )}}{sin^{2}{left (t right )}}$$
Тригонометрическая часть
2 / 1 2
cos (t)*|——- – 2*cos (t)|
| 2 |
sin (t) /
$$left(- 2 cos^{2}{left (t right )} + frac{1}{sin^{2}{left (t right )}}right) cos^{2}{left (t right )}$$
Раскрыть выражение
2 / 4 4
cos (t)*cos (t) + sin (t)/
—————————
2
sin (t)
$$frac{cos^{2}{left (t right )}}{sin^{2}{left (t right )}} left(sin^{4}{left (t right )} + cos^{4}{left (t right )}right)$$
