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

/ 3 3 5 5 / 5 3 7 7 3 5 / 5 3 7 7 3 5 / 3 7 7 3 9 9 5 5
– 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)/

$$left(6 sin^{5}{left (a right )} cos{left (a right )} – 20 sin^{3}{left (a right )} cos^{3}{left (a right )} + 6 sin{left (a right )} cos^{5}{left (a right )}right) left(- 8 sin^{7}{left (a right )} cos{left (a right )} + 56 sin^{5}{left (a right )} cos^{3}{left (a right )} – 56 sin^{3}{left (a right )} cos^{5}{left (a right )} + 8 sin{left (a right )} cos^{7}{left (a right )}right) + left(- 8 sin^{7}{left (a right )} cos{left (a right )} + 56 sin^{5}{left (a right )} cos^{3}{left (a right )} – 56 sin^{3}{left (a right )} cos^{5}{left (a right )} + 8 sin{left (a right )} cos^{7}{left (a right )}right) left(10 sin^{9}{left (a right )} cos{left (a right )} – 120 sin^{7}{left (a right )} cos^{3}{left (a right )} + 252 sin^{5}{left (a right )} cos^{5}{left (a right )} – 120 sin^{3}{left (a right )} cos^{7}{left (a right )} + 10 sin{left (a right )} cos^{9}{left (a right )}right)$$
   
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Iri5
Опыт выполнения студенческих работ с 2005 года. Юриспруденциия (контрольные, рефераты, курсовые, дипломные работы, отчеты по практике, задачи по всем отраслям права). Психология (рефераты, контрольные, эссе, курсовые).