Дано
$$cos{left (2 a right )} + frac{cos{left (6 a right )}}{sin{left (4 a right )}} + sin{left (2 a right )} + sin{left (6 a right )} + cos{left (4 a right )}$$
Подстановка условия
$$cos{left (2 a right )} + frac{cos{left (6 a right )}}{sin{left (4 a right )}} + sin{left (2 a right )} + sin{left (6 a right )} + cos{left (4 a right )}$$
cos(2*(-2)) + cos(6*(-2))/sin(4*(-2)) + sin(2*(-2)) + sin(6*(-2)) + cos(4*(-2))
$$cos{left (2 (-2) right )} + frac{cos{left (6 (-2) right )}}{sin{left (4 (-2) right )}} + sin{left (2 (-2) right )} + sin{left (6 (-2) right )} + cos{left (4 (-2) right )}$$
cos(2*(-2)) + cos(6*(-2))/sin(4*(-2)) + sin(2*(-2)) + sin(6*(-2)) + cos(4*(-2))
$$frac{cos{left (-2 cdot 6 right )}}{sin{left (-2 cdot 4 right )}} + cos{left (-2 cdot 2 right )} + sin{left (-2 cdot 2 right )} + sin{left (-2 cdot 6 right )} + cos{left (-2 cdot 4 right )}$$
-sin(4) – sin(12) – cos(12)/sin(8) + cos(4) + cos(8)
$$- frac{cos{left (12 right )}}{sin{left (8 right )}} + cos{left (4 right )} + cos{left (8 right )} – sin{left (12 right )} – sin{left (4 right )}$$
Степени
$$sin{left (2 a right )} + sin{left (6 a right )} + cos{left (2 a right )} + cos{left (4 a right )} + frac{cos{left (6 a right )}}{sin{left (4 a right )}}$$
Численный ответ
cos(6*a)/sin(4*a) + cos(2*a) + cos(4*a) + sin(2*a) + sin(6*a)
Рациональный знаменатель
$$frac{1}{sin{left (4 a right )}} left(sin{left (2 a right )} sin{left (4 a right )} + sin{left (4 a right )} sin{left (6 a right )} + sin{left (4 a right )} cos{left (2 a right )} + sin{left (4 a right )} cos{left (4 a right )} + cos{left (6 a right )}right)$$
Объединение рациональных выражений
$$frac{1}{sin{left (4 a right )}} left(sin{left (2 a right )} sin{left (4 a right )} + sin{left (4 a right )} sin{left (6 a right )} + sin{left (4 a right )} cos{left (2 a right )} + sin{left (4 a right )} cos{left (4 a right )} + cos{left (6 a right )}right)$$
Общее упрощение
cos(6*a)
——– + cos(2*a) + cos(4*a) + sin(2*a) + sin(6*a)
sin(4*a)
$$sin{left (2 a right )} + sin{left (6 a right )} + cos{left (2 a right )} + cos{left (4 a right )} + frac{cos{left (6 a right )}}{sin{left (4 a right )}}$$
Соберем выражение
$$sin{left (2 a right )} + sin{left (6 a right )} + cos{left (2 a right )} + cos{left (4 a right )} + cos{left (6 a right )} csc{left (4 a right )}$$
cos(6*a)
——– + cos(2*a) + cos(4*a) + sin(2*a) + sin(6*a)
sin(4*a)
$$sin{left (2 a right )} + sin{left (6 a right )} + cos{left (2 a right )} + cos{left (4 a right )} + frac{cos{left (6 a right )}}{sin{left (4 a right )}}$$
Комбинаторика
cos(2*a)*sin(4*a) + cos(4*a)*sin(4*a) + sin(2*a)*sin(4*a) + sin(4*a)*sin(6*a) + cos(6*a)
—————————————————————————————-
sin(4*a)
$$frac{1}{sin{left (4 a right )}} left(sin{left (2 a right )} sin{left (4 a right )} + sin{left (4 a right )} sin{left (6 a right )} + sin{left (4 a right )} cos{left (2 a right )} + sin{left (4 a right )} cos{left (4 a right )} + cos{left (6 a right )}right)$$
Общий знаменатель
cos(6*a)
——– + cos(2*a) + cos(4*a) + sin(2*a) + sin(6*a)
sin(4*a)
$$sin{left (2 a right )} + sin{left (6 a right )} + cos{left (2 a right )} + cos{left (4 a right )} + frac{cos{left (6 a right )}}{sin{left (4 a right )}}$$
Тригонометрическая часть
cos(6*a)
——– + cos(2*a) + cos(4*a) + sin(2*a) + sin(6*a)
sin(4*a)
$$sin{left (2 a right )} + sin{left (6 a right )} + cos{left (2 a right )} + cos{left (4 a right )} + frac{cos{left (6 a right )}}{sin{left (4 a right )}}$$
Раскрыть выражение
6 6 4 2 2 4
2 4 4 2 cos (a) – sin (a) – 15*cos (a)*sin (a) + 15*cos (a)*sin (a) 3 3 2 2 5 5
cos (a) + cos (a) + sin (a) – sin (a) + ———————————————————– – 20*cos (a)*sin (a) – 6*cos (a)*sin (a) + 2*cos(a)*sin(a) + 6*cos (a)*sin(a) + 6*sin (a)*cos(a)
3 3
– 4*sin (a)*cos(a) + 4*cos (a)*sin(a)
$$6 sin^{5}{left (a right )} cos{left (a right )} + sin^{4}{left (a right )} – 20 sin^{3}{left (a right )} cos^{3}{left (a right )} – 6 sin^{2}{left (a right )} cos^{2}{left (a right )} – sin^{2}{left (a right )} + 6 sin{left (a right )} cos^{5}{left (a right )} + 2 sin{left (a right )} cos{left (a right )} + cos^{4}{left (a right )} + cos^{2}{left (a right )} + frac{- sin^{6}{left (a right )} + 15 sin^{4}{left (a right )} cos^{2}{left (a right )} – 15 sin^{2}{left (a right )} cos^{4}{left (a right )} + cos^{6}{left (a right )}}{- 4 sin^{3}{left (a right )} cos{left (a right )} + 4 sin{left (a right )} cos^{3}{left (a right )}}$$
