Дано
$$frac{1}{4} left(sin{left (2 x right )} + sin{left (4 x right )} – sin{left (6 x right )}right) sin{left (x right )} sin{left (2 x right )}$$
Подстановка условия
$$frac{1}{4} left(sin{left (2 x right )} + sin{left (4 x right )} – sin{left (6 x right )}right) sin{left (x right )} sin{left (2 x right )}$$
(((sin(2*(-4)) + sin(4*(-4)) – sin(6*(-4)))/4)*sin((-4)))*sin(2*(-4))
$$frac{1}{4} left(sin{left (2 (-4) right )} + sin{left (4 (-4) right )} – sin{left (6 (-4) right )}right) sin{left ((-4) right )} sin{left (2 (-4) right )}$$
(((sin(2*(-4)) + sin(4*(-4)) – sin(6*(-4)))/4)*sin(-4))*sin(2*(-4))
$$frac{1}{4} left(- sin{left (-4 cdot 6 right )} + sin{left (-4 cdot 2 right )} + sin{left (-4 cdot 4 right )}right) sin{left (-4 right )} sin{left (-4 cdot 2 right )}$$
(-sin(8)/4 – sin(16)/4 + sin(24)/4)*sin(4)*sin(8)
$$left(- frac{1}{4} sin{left (8 right )} + frac{1}{4} sin{left (24 right )} – frac{1}{4} sin{left (16 right )}right) sin{left (4 right )} sin{left (8 right )}$$
Степени
$$left(frac{1}{4} sin{left (2 x right )} + frac{1}{4} sin{left (4 x right )} – frac{1}{4} sin{left (6 x right )}right) sin{left (x right )} sin{left (2 x right )}$$
Численный ответ
0.25*(-sin(6*x) + sin(2*x) + sin(4*x))*sin(x)*sin(2*x)
Объединение рациональных выражений
$$left(frac{1}{4} sin{left (2 x right )} + frac{1}{4} sin{left (4 x right )} – frac{1}{4} sin{left (6 x right )}right) sin{left (x right )} sin{left (2 x right )}$$
Соберем выражение
$$left(frac{1}{4} sin{left (2 x right )} + frac{1}{4} sin{left (4 x right )} – frac{1}{4} sin{left (6 x right )}right) sin{left (x right )} sin{left (2 x right )}$$
sin(7*x) sin(5*x) sin(x) sin(9*x) 3*sin(3*x)
– ——– – ——– + —— + ——– + ———-
8 16 16 16 16
$$frac{1}{16} sin{left (x right )} + frac{3}{16} sin{left (3 x right )} – frac{1}{16} sin{left (5 x right )} – frac{1}{8} sin{left (7 x right )} + frac{1}{16} sin{left (9 x right )}$$
Общий знаменатель
2
sin (2*x)*sin(x) sin(x)*sin(2*x)*sin(6*x) sin(x)*sin(2*x)*sin(4*x)
—————- – ———————— + ————————
4 4 4
$$frac{1}{4} sin{left (x right )} sin^{2}{left (2 x right )} + frac{1}{4} sin{left (x right )} sin{left (2 x right )} sin{left (4 x right )} – frac{1}{4} sin{left (x right )} sin{left (2 x right )} sin{left (6 x right )}$$
Тригонометрическая часть
/ cos(5*x) cos(x) cos(7*x)
|- ——– + —— + ——–|*sin(2*x)
4 8 8 /
$$left(frac{1}{8} cos{left (x right )} – frac{1}{4} cos{left (5 x right )} + frac{1}{8} cos{left (7 x right )}right) sin{left (2 x right )}$$
Раскрыть выражение
2 / 5 5 3 3 3 3
sin (x)* – 6*cos (x)*sin(x) – 6*sin (x)*cos(x) – 4*sin (x)*cos(x) + 2*cos(x)*sin(x) + 4*cos (x)*sin(x) + 20*cos (x)*sin (x)/*cos(x)
———————————————————————————————————————————–
2
$$frac{1}{2} left(- 6 sin^{5}{left (x right )} cos{left (x right )} + 20 sin^{3}{left (x right )} cos^{3}{left (x right )} – 4 sin^{3}{left (x right )} cos{left (x right )} – 6 sin{left (x right )} cos^{5}{left (x right )} + 4 sin{left (x right )} cos^{3}{left (x right )} + 2 sin{left (x right )} cos{left (x right )}right) sin^{2}{left (x right )} cos{left (x right )}$$
