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