Дано
$$sin{left (6 a right )} sin{left (8 a right )} + sin{left (8 a right )} sin{left (10 a right )}$$
Подстановка условия
$$sin{left (6 a right )} sin{left (8 a right )} + sin{left (8 a right )} sin{left (10 a right )}$$
sin(10*(1))*sin(8*(1)) + sin(8*(1))*sin(6*(1))
$$sin{left (6 (1) right )} sin{left (8 (1) right )} + sin{left (8 (1) right )} sin{left (10 (1) right )}$$
sin(10)*sin(8) + sin(8)*sin(6)
$$sin{left (8 right )} sin{left (10 right )} + sin{left (6 right )} sin{left (8 right )}$$
sin(6)*sin(8) + sin(8)*sin(10)
$$sin{left (8 right )} sin{left (10 right )} + sin{left (6 right )} sin{left (8 right )}$$
Численный ответ
sin(6*a)*sin(8*a) + sin(8*a)*sin(10*a)
Объединение рациональных выражений
$$left(sin{left (6 a right )} + sin{left (10 a right )}right) sin{left (8 a right )}$$
Общее упрощение
(sin(6*a) + sin(10*a))*sin(8*a)
$$left(sin{left (6 a right )} + sin{left (10 a right )}right) sin{left (8 a right )}$$
Соберем выражение
$$cos{left (2 a right )} – frac{1}{2} cos{left (14 a right )} – frac{1}{2} cos{left (18 a right )}$$
Комбинаторика
(sin(6*a) + sin(10*a))*sin(8*a)
$$left(sin{left (6 a right )} + sin{left (10 a right )}right) sin{left (8 a right )}$$
Раскрыть выражение
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– 20*cos (a)*sin (a) + 6*cos (a)*sin(a) + 6*sin (a)*cos(a)/* – 56*cos (a)*sin (a) – 8*sin (a)*cos(a) + 8*cos (a)*sin(a) + 56*cos (a)*sin (a)/ + – 56*cos (a)*sin (a) – 8*sin (a)*cos(a) + 8*cos (a)*sin(a) + 56*cos (a)*sin (a)/* – 120*cos (a)*sin (a) – 120*cos (a)*sin (a) + 10*cos (a)*sin(a) + 10*sin (a)*cos(a) + 252*cos (a)*sin (a)/
$$left(6 sin^{5}{left (a right )} cos{left (a right )} – 20 sin^{3}{left (a right )} cos^{3}{left (a right )} + 6 sin{left (a right )} cos^{5}{left (a right )}right) left(- 8 sin^{7}{left (a right )} cos{left (a right )} + 56 sin^{5}{left (a right )} cos^{3}{left (a right )} – 56 sin^{3}{left (a right )} cos^{5}{left (a right )} + 8 sin{left (a right )} cos^{7}{left (a right )}right) + left(- 8 sin^{7}{left (a right )} cos{left (a right )} + 56 sin^{5}{left (a right )} cos^{3}{left (a right )} – 56 sin^{3}{left (a right )} cos^{5}{left (a right )} + 8 sin{left (a right )} cos^{7}{left (a right )}right) left(10 sin^{9}{left (a right )} cos{left (a right )} – 120 sin^{7}{left (a right )} cos^{3}{left (a right )} + 252 sin^{5}{left (a right )} cos^{5}{left (a right )} – 120 sin^{3}{left (a right )} cos^{7}{left (a right )} + 10 sin{left (a right )} cos^{9}{left (a right )}right)$$
