Дано
$$frac{1}{144} left(- 20 sin^{frac{18}{5}}{left (2 x right )} – – 45 sin^{frac{8}{5}}{left (2 x right )}right)$$
Подстановка условия
$$frac{1}{144} left(- 20 sin^{frac{18}{5}}{left (2 x right )} – – 45 sin^{frac{8}{5}}{left (2 x right )}right)$$
(-20*sin(2*(1))^(18/5) – (-1)*45*sin(2*(1))^(8/5))/144
$$frac{1}{144} left(- 20 sin^{frac{18}{5}}{left (2 (1) right )} – – 45 sin^{frac{8}{5}}{left (2 (1) right )}right)$$
(-20*sin(2)^(18/5) – (-1)*45*sin(2)^(8/5))/144
$$frac{1}{144} left(- 20 sin^{frac{18}{5}}{left (2 right )} – – 45 sin^{frac{8}{5}}{left (2 right )}right)$$
-5*sin(2)^(18/5)/36 + 5*sin(2)^(8/5)/16
$$- frac{5}{36} sin^{frac{18}{5}}{left (2 right )} + frac{5}{16} sin^{frac{8}{5}}{left (2 right )}$$
Степени
$$- frac{5}{36} sin^{frac{18}{5}}{left (2 x right )} + frac{5}{16} sin^{frac{8}{5}}{left (2 x right )}$$
Численный ответ
0.3125*sin(2*x)^1.6 – 0.138888888888889*sin(2*x)^3.6
Рациональный знаменатель
$$- frac{5}{36} sin^{frac{18}{5}}{left (2 x right )} + frac{5}{16} sin^{frac{8}{5}}{left (2 x right )}$$
Объединение рациональных выражений
$$frac{5}{144} left(- 4 sin^{2}{left (2 x right )} + 9right) sin^{frac{8}{5}}{left (2 x right )}$$
Общее упрощение
8/5
5*sin (2*x)*(7 + 2*cos(4*x))
——————————
144
$$frac{5}{144} left(2 cos{left (4 x right )} + 7right) sin^{frac{8}{5}}{left (2 x right )}$$
Соберем выражение
$$- frac{5}{36} sin^{frac{18}{5}}{left (2 x right )} – – frac{5}{16} sin^{frac{8}{5}}{left (2 x right )}$$
18/5 8/5
5*sin (2*x) 5*sin (2*x)
– ————– + ————-
36 16
$$- frac{5}{36} sin^{frac{18}{5}}{left (2 x right )} + frac{5}{16} sin^{frac{8}{5}}{left (2 x right )}$$
Общий знаменатель
18/5 8/5
5*sin (2*x) 5*sin (2*x)
– ————– + ————-
36 16
$$- frac{5}{36} sin^{frac{18}{5}}{left (2 x right )} + frac{5}{16} sin^{frac{8}{5}}{left (2 x right )}$$
Тригонометрическая часть
8/5 / 2
5*sin (2*x)*9 – 4*sin (2*x)/
——————————-
144
$$frac{5}{144} left(- 4 sin^{2}{left (2 x right )} + 9right) sin^{frac{8}{5}}{left (2 x right )}$$
Комбинаторика
8/5
-5*sin (2*x)*(-3 + 2*sin(2*x))*(3 + 2*sin(2*x))
————————————————-
144
$$- frac{5}{144} left(2 sin{left (2 x right )} – 3right) left(2 sin{left (2 x right )} + 3right) sin^{frac{8}{5}}{left (2 x right )}$$
Раскрыть выражение
3/5 18/5 18/5 3/5 8/5 8/5
10*2 *cos (x)*sin (x) 5*2 *cos (x)*sin (x)
– —————————– + ————————–
9 8
$$- frac{10}{9} 2^{frac{3}{5}} sin^{frac{18}{5}}{left (x right )} cos^{frac{18}{5}}{left (x right )} + frac{5}{8} 2^{frac{3}{5}} sin^{frac{8}{5}}{left (x right )} cos^{frac{8}{5}}{left (x right )}$$
