Дано
$$- sin{left (5 a right )} + sin{left (7 a right )} – frac{4}{3} sin{left (9 a right )} + sin{left (3 a right )}$$
Подстановка условия
$$- sin{left (5 a right )} + sin{left (7 a right )} – frac{4}{3} sin{left (9 a right )} + sin{left (3 a right )}$$
sin(7*(-3/2)) – sin(5*(-3/2)) – 4*sin(9*(-3/2))/3 + sin(3*(-3/2))
$$- sin{left (5 (-3/2) right )} + sin{left (7 (-3/2) right )} – frac{4}{3} sin{left (9 (-3/2) right )} + sin{left (3 (-3/2) right )}$$
sin(7*(-3)/2) – sin(5*(-3)/2) – 4*sin(9*(-3)/2)/3 + sin(3*(-3)/2)
$$sin{left (frac{-9}{2} right )} + – frac{4}{3} sin{left (frac{-27}{2} right )} + sin{left (frac{-21}{2} right )} – sin{left (frac{-15}{2} right )}$$
-sin(9/2) – sin(21/2) + 4*sin(27/2)/3 + sin(15/2)
$$- sin{left (frac{21}{2} right )} + sin{left (frac{15}{2} right )} – sin{left (frac{9}{2} right )} + frac{4}{3} sin{left (frac{27}{2} right )}$$
Степени
$$sin{left (3 a right )} – sin{left (5 a right )} + sin{left (7 a right )} – frac{4}{3} sin{left (9 a right )}$$
Численный ответ
-sin(5*a) – 1.33333333333333*sin(9*a) + sin(3*a) + sin(7*a)
Рациональный знаменатель
$$sin{left (3 a right )} – sin{left (5 a right )} + sin{left (7 a right )} – frac{4}{3} sin{left (9 a right )}$$
Объединение рациональных выражений
$$frac{1}{3} left(3 sin{left (3 a right )} – 3 sin{left (5 a right )} + 3 sin{left (7 a right )} – 4 sin{left (9 a right )}right)$$
Общее упрощение
4*sin(9*a)
-sin(5*a) – ———- + sin(3*a) + sin(7*a)
3
$$sin{left (3 a right )} – sin{left (5 a right )} + sin{left (7 a right )} – frac{4}{3} sin{left (9 a right )}$$
Соберем выражение
$$sin{left (3 a right )} – sin{left (5 a right )} + sin{left (7 a right )} – frac{4}{3} sin{left (9 a right )}$$
Общий знаменатель
4*sin(9*a)
-sin(5*a) – ———- + sin(3*a) + sin(7*a)
3
$$sin{left (3 a right )} – sin{left (5 a right )} + sin{left (7 a right )} – frac{4}{3} sin{left (9 a right )}$$
Комбинаторика
-4*sin(9*a) – 3*sin(5*a) + 3*sin(3*a) + 3*sin(7*a)
————————————————–
3
$$frac{1}{3} left(3 sin{left (3 a right )} – 3 sin{left (5 a right )} + 3 sin{left (7 a right )} – 4 sin{left (9 a right )}right)$$
Тригонометрическая часть
4*sin(9*a)
-sin(5*a) – ———- + sin(3*a) + sin(7*a)
3
$$sin{left (3 a right )} – sin{left (5 a right )} + sin{left (7 a right )} – frac{4}{3} sin{left (9 a right )}$$
Раскрыть выражение
9
3 5 7 4*sin (a) 4 5 4 3 8 4 2 6 2 3 2 5 2 7 6 3
– sin (a) – sin (a) – sin (a) – ——— – 168*cos (a)*sin (a) – 35*cos (a)*sin (a) – 12*cos (a)*sin(a) – 5*cos (a)*sin(a) + 3*cos (a)*sin(a) + 7*cos (a)*sin(a) + 10*cos (a)*sin (a) + 21*cos (a)*sin (a) + 48*cos (a)*sin (a) + 112*cos (a)*sin (a)
3
$$- frac{4}{3} sin^{9}{left (a right )} + 48 sin^{7}{left (a right )} cos^{2}{left (a right )} – sin^{7}{left (a right )} – 168 sin^{5}{left (a right )} cos^{4}{left (a right )} + 21 sin^{5}{left (a right )} cos^{2}{left (a right )} – sin^{5}{left (a right )} + 112 sin^{3}{left (a right )} cos^{6}{left (a right )} – 35 sin^{3}{left (a right )} cos^{4}{left (a right )} + 10 sin^{3}{left (a right )} cos^{2}{left (a right )} – sin^{3}{left (a right )} – 12 sin{left (a right )} cos^{8}{left (a right )} + 7 sin{left (a right )} cos^{6}{left (a right )} – 5 sin{left (a right )} cos^{4}{left (a right )} + 3 sin{left (a right )} cos^{2}{left (a right )}$$
