Дано
$$- frac{75}{4} sin{left (2 x right )} sin{left (4 x right )} + frac{1}{2} 75 sin^{2}{left (2 x right )} cos{left (2 x right )}$$
Подстановка условия
$$- frac{75}{4} sin{left (2 x right )} sin{left (4 x right )} + frac{1}{2} 75 sin^{2}{left (2 x right )} cos{left (2 x right )}$$
((75*cos(2*(1/2)))*sin(2*(1/2))^2)/2 – (75*sin(4*(1/2)))*sin(2*(1/2))/4
$$- frac{75}{4} sin{left (2 (1/2) right )} sin{left (4 (1/2) right )} + frac{1}{2} 75 sin^{2}{left (2 (1/2) right )} cos{left (2 (1/2) right )}$$
((75*cos(2/2))*sin(2/2)^2)/2 – (75*sin(4/2))*sin(2/2)/4
$$- frac{75}{4} sin{left (frac{2}{2} right )} sin{left (frac{4}{2} right )} + frac{1}{2} 75 sin^{2}{left (frac{2}{2} right )} cos{left (frac{2}{2} right )}$$
-75*sin(1)*sin(2)/4 + 75*sin(1)^2*cos(1)/2
$$- frac{75}{4} sin{left (1 right )} sin{left (2 right )} + frac{75}{2} sin^{2}{left (1 right )} cos{left (1 right )}$$
Степени
$$frac{75}{2} sin^{2}{left (2 x right )} cos{left (2 x right )} – frac{75}{4} sin{left (2 x right )} sin{left (4 x right )}$$
Численный ответ
37.5*sin(2*x)^2*cos(2*x) – 18.75*sin(2*x)*sin(4*x)
Рациональный знаменатель
$$frac{75}{2} sin^{2}{left (2 x right )} cos{left (2 x right )} – frac{75}{4} sin{left (2 x right )} sin{left (4 x right )}$$
Объединение рациональных выражений
$$frac{75}{4} left(2 sin{left (2 x right )} cos{left (2 x right )} – sin{left (4 x right )}right) sin{left (2 x right )}$$
Общее упрощение
$$0$$
Соберем выражение
$$0$$
Общий знаменатель
2
75*sin(2*x)*sin(4*x) 75*sin (2*x)*cos(2*x)
– ——————– + ———————
4 2
$$frac{75}{2} sin^{2}{left (2 x right )} cos{left (2 x right )} – frac{75}{4} sin{left (2 x right )} sin{left (4 x right )}$$
Тригонометрическая часть
$$0$$
Комбинаторика
75*(-sin(4*x) + 2*cos(2*x)*sin(2*x))*sin(2*x)
———————————————
4
$$frac{75}{4} left(2 sin{left (2 x right )} cos{left (2 x right )} – sin{left (4 x right )}right) sin{left (2 x right )}$$
Раскрыть выражение
/ 3 3
2 2 / 2 2 75* – 4*sin (x)*cos(x) + 4*cos (x)*sin(x)/*cos(x)*sin(x)
150*cos (x)*sin (x)*cos (x) – sin (x)/ – ——————————————————–
2
$$- frac{75}{2} left(- 4 sin^{3}{left (x right )} cos{left (x right )} + 4 sin{left (x right )} cos^{3}{left (x right )}right) sin{left (x right )} cos{left (x right )} + 150 left(- sin^{2}{left (x right )} + cos^{2}{left (x right )}right) sin^{2}{left (x right )} cos^{2}{left (x right )}$$
