Дано
$$frac{1}{- cos{left (8 x right )} + 1} left(sin{left (2 x right )} + sin{left (6 x right )}right) left(cos{left (2 x right )} – cos{left (6 x right )}right)$$
Подстановка условия
$$frac{1}{- cos{left (8 x right )} + 1} left(sin{left (2 x right )} + sin{left (6 x right )}right) left(cos{left (2 x right )} – cos{left (6 x right )}right)$$
((sin(2*(-3)) + sin(6*(-3)))*(cos(2*(-3)) – cos(6*(-3))))/(1 – cos(8*(-3)))
$$frac{1}{- cos{left (8 (-3) right )} + 1} left(sin{left (2 (-3) right )} + sin{left (6 (-3) right )}right) left(cos{left (2 (-3) right )} – cos{left (6 (-3) right )}right)$$
((sin(2*(-3)) + sin(6*(-3)))*(cos(2*(-3)) – cos(6*(-3))))/(1 – cos(8*(-3)))
$$frac{1}{- cos{left (-3 cdot 8 right )} + 1} left(sin{left (-3 cdot 2 right )} + sin{left (-3 cdot 6 right )}right) left(- cos{left (-3 cdot 6 right )} + cos{left (-3 cdot 2 right )}right)$$
(-cos(18) + cos(6))*(-sin(6) – sin(18))/(1 – cos(24))
$$frac{1}{- cos{left (24 right )} + 1} left(- sin{left (6 right )} – sin{left (18 right )}right) left(- cos{left (18 right )} + cos{left (6 right )}right)$$
Численный ответ
(-cos(6*x) + cos(2*x))*(sin(2*x) + sin(6*x))/(1.0 – cos(8*x))
Общее упрощение
-(-cos(6*x) + cos(2*x))*(sin(2*x) + sin(6*x))
———————————————-
-1 + cos(8*x)
$$- frac{1}{cos{left (8 x right )} – 1} left(sin{left (2 x right )} + sin{left (6 x right )}right) left(cos{left (2 x right )} – cos{left (6 x right )}right)$$
Соберем выражение
$$- frac{3 sin{left (4 x right )}}{2 cos{left (8 x right )} – 2} + frac{sin{left (12 x right )}}{2 cos{left (8 x right )} – 2}$$
Общий знаменатель
-(cos(2*x)*sin(2*x) + cos(2*x)*sin(6*x) – cos(6*x)*sin(2*x) – cos(6*x)*sin(6*x))
———————————————————————————
-1 + cos(8*x)
$$- frac{1}{cos{left (8 x right )} – 1} left(sin{left (2 x right )} cos{left (2 x right )} – sin{left (2 x right )} cos{left (6 x right )} + sin{left (6 x right )} cos{left (2 x right )} – sin{left (6 x right )} cos{left (6 x right )}right)$$
Комбинаторика
-(-cos(6*x) + cos(2*x))*(sin(2*x) + sin(6*x))
———————————————-
-1 + cos(8*x)
$$- frac{1}{cos{left (8 x right )} – 1} left(sin{left (2 x right )} + sin{left (6 x right )}right) left(cos{left (2 x right )} – cos{left (6 x right )}right)$$
Раскрыть выражение
/ 3 3 5 5 / 2 6 6 2 2 4 4 2
– 20*cos (x)*sin (x) + 2*cos(x)*sin(x) + 6*cos (x)*sin(x) + 6*sin (x)*cos(x)/*cos (x) + sin (x) – cos (x) – sin (x) – 15*cos (x)*sin (x) + 15*cos (x)*sin (x)/
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8 8 4 4 2 6 6 2
1 – cos (x) – sin (x) – 70*cos (x)*sin (x) + 28*cos (x)*sin (x) + 28*cos (x)*sin (x)
$$frac{left(6 sin^{5}{left (x right )} cos{left (x right )} – 20 sin^{3}{left (x right )} cos^{3}{left (x right )} + 6 sin{left (x right )} cos^{5}{left (x right )} + 2 sin{left (x right )} cos{left (x right )}right) left(sin^{6}{left (x right )} – 15 sin^{4}{left (x right )} cos^{2}{left (x right )} + 15 sin^{2}{left (x right )} cos^{4}{left (x right )} – sin^{2}{left (x right )} – cos^{6}{left (x right )} + cos^{2}{left (x right )}right)}{- sin^{8}{left (x right )} + 28 sin^{6}{left (x right )} cos^{2}{left (x right )} – 70 sin^{4}{left (x right )} cos^{4}{left (x right )} + 28 sin^{2}{left (x right )} cos^{6}{left (x right )} – cos^{8}{left (x right )} + 1}$$
