Дано
$$a cos^{3}{left (2 right )} sin{left (6 a right )} + sin^{3}{left (2 a right )} cos{left (6 a right )}$$
Подстановка условия
$$a cos^{3}{left (2 right )} sin{left (6 a right )} + sin^{3}{left (2 a right )} cos{left (6 a right )}$$
sin(2*(1/2))^3*cos(6*(1/2)) + (cos(2)^3*(1/2))*sin(6*(1/2))
$$(1/2) cos^{3}{left (2 right )} sin{left (6 (1/2) right )} + sin^{3}{left (2 (1/2) right )} cos{left (6 (1/2) right )}$$
sin(2/2)^3*cos(6/2) + (cos(2)^3/2)*sin(6/2)
$$sin^{3}{left (frac{2}{2} right )} cos{left (frac{6}{2} right )} + frac{1}{2} cos^{3}{left (2 right )} sin{left (frac{6}{2} right )}$$
sin(1)^3*cos(3) + cos(2)^3*sin(3)/2
$$sin^{3}{left (1 right )} cos{left (3 right )} + frac{1}{2} sin{left (3 right )} cos^{3}{left (2 right )}$$
Степени
$$a sin{left (6 a right )} cos^{3}{left (2 right )} + sin^{3}{left (2 a right )} cos{left (6 a right )}$$
Численный ответ
sin(2*a)^3*cos(6*a) – 0.0720675557477653*a*sin(6*a)
Рациональный знаменатель
$$a sin{left (6 a right )} cos^{3}{left (2 right )} + sin^{3}{left (2 a right )} cos{left (6 a right )}$$
Объединение рациональных выражений
$$a sin{left (6 a right )} cos^{3}{left (2 right )} + sin^{3}{left (2 a right )} cos{left (6 a right )}$$
Общее упрощение
3 3
sin (2*a)*cos(6*a) + a*cos (2)*sin(6*a)
$$a sin{left (6 a right )} cos^{3}{left (2 right )} + sin^{3}{left (2 a right )} cos{left (6 a right )}$$
Соберем выражение
$$frac{a}{8} sin{left (6 a – 6 right )} + frac{3 a}{8} sin{left (6 a – 2 right )} + frac{3 a}{8} sin{left (6 a + 2 right )} + frac{a}{8} sin{left (6 a + 6 right )} – frac{3}{8} sin{left (4 a right )} + frac{3}{8} sin{left (8 a right )} – frac{1}{8} sin{left (12 a right )}$$
Общий знаменатель
3 3
sin (2*a)*cos(6*a) + a*cos (2)*sin(6*a)
$$a sin{left (6 a right )} cos^{3}{left (2 right )} + sin^{3}{left (2 a right )} cos{left (6 a right )}$$
Тригонометрическая часть
3 3
sin (2*a)*cos(6*a) + a*cos (2)*sin(6*a)
$$a sin{left (6 a right )} cos^{3}{left (2 right )} + sin^{3}{left (2 a right )} cos{left (6 a right )}$$
Комбинаторика
3 3
sin (2*a)*cos(6*a) + a*cos (2)*sin(6*a)
$$a sin{left (6 a right )} cos^{3}{left (2 right )} + sin^{3}{left (2 a right )} cos{left (6 a right )}$$
Раскрыть выражение
3 / 3 3 5 5 3 3 / 6 6 4 2 2 4
a*cos (2)* – 20*cos (a)*sin (a) + 6*cos (a)*sin(a) + 6*sin (a)*cos(a)/ + 8*cos (a)*sin (a)*cos (a) – sin (a) – 15*cos (a)*sin (a) + 15*cos (a)*sin (a)/
$$a left(6 sin^{5}{left (a right )} cos{left (a right )} – 20 sin^{3}{left (a right )} cos^{3}{left (a right )} + 6 sin{left (a right )} cos^{5}{left (a right )}right) cos^{3}{left (2 right )} + 8 left(- sin^{6}{left (a right )} + 15 sin^{4}{left (a right )} cos^{2}{left (a right )} – 15 sin^{2}{left (a right )} cos^{4}{left (a right )} + cos^{6}{left (a right )}right) sin^{3}{left (a right )} cos^{3}{left (a right )}$$
