Дано
$$sin{left (a right )} + 1 – cos{left (2 a right )} – frac{1}{2} sin^{2}{left (a right )} sin{left (3 a right )} + sin{left (a right )} – 1$$
Подстановка условия
$$sin{left (a right )} + 1 – cos{left (2 a right )} – frac{1}{2} sin^{2}{left (a right )} sin{left (3 a right )} + sin{left (a right )} – 1$$
1 + sin((1/4)) – cos(2*(1/4)) – sin(3*(1/4))/2*sin((1/4))^2 + sin((1/4)) – 1
$$sin{left ((1/4) right )} + 1 – cos{left (2 (1/4) right )} – frac{1}{2} sin^{2}{left ((1/4) right )} sin{left (3 (1/4) right )} + sin{left ((1/4) right )} – 1$$
1 + sin(1/4) – cos(2/4) – sin(3/4)/2*sin(1/4)^2 + sin(1/4) – 1
$$-1 + sin{left (frac{1}{4} right )} + – frac{1}{2} sin^{2}{left (frac{1}{4} right )} sin{left (frac{3}{4} right )} + – cos{left (frac{2}{4} right )} + sin{left (frac{1}{4} right )} + 1$$
-cos(1/2) + 2*sin(1/4) – sin(1/4)^2*sin(3/4)/2
$$- cos{left (frac{1}{2} right )} – frac{1}{2} sin^{2}{left (frac{1}{4} right )} sin{left (frac{3}{4} right )} + 2 sin{left (frac{1}{4} right )}$$
Степени
$$- frac{1}{2} sin^{2}{left (a right )} sin{left (3 a right )} + 2 sin{left (a right )} – cos{left (2 a right )}$$
Численный ответ
-cos(2*a) + 2*sin(a) – 0.5*sin(a)^2*sin(3*a)
Рациональный знаменатель
$$- frac{1}{2} sin^{2}{left (a right )} sin{left (3 a right )} + 2 sin{left (a right )} – cos{left (2 a right )}$$
Объединение рациональных выражений
$$frac{1}{2} left(- sin^{2}{left (a right )} sin{left (3 a right )} + 4 sin{left (a right )} – 2 cos{left (2 a right )}right)$$
Общее упрощение
2
sin (a)*sin(3*a)
-cos(2*a) + 2*sin(a) – —————-
2
$$- frac{1}{2} sin^{2}{left (a right )} sin{left (3 a right )} + 2 sin{left (a right )} – cos{left (2 a right )}$$
Соберем выражение
$$- frac{1}{2} sin^{2}{left (a right )} sin{left (3 a right )} + 2 sin{left (a right )} – cos{left (2 a right )}$$
sin(3*a) sin(5*a) 17*sin(a)
-cos(2*a) – ——– + ——– + ———
4 8 8
$$frac{17}{8} sin{left (a right )} – frac{1}{4} sin{left (3 a right )} + frac{1}{8} sin{left (5 a right )} – cos{left (2 a right )}$$
Общий знаменатель
2
sin (a)*sin(3*a)
-cos(2*a) + 2*sin(a) – —————-
2
$$- frac{1}{2} sin^{2}{left (a right )} sin{left (3 a right )} + 2 sin{left (a right )} – cos{left (2 a right )}$$
Комбинаторика
/ 2
– -4*sin(a) + 2*cos(2*a) + sin (a)*sin(3*a)/
———————————————
2
$$- frac{1}{2} left(sin^{2}{left (a right )} sin{left (3 a right )} – 4 sin{left (a right )} + 2 cos{left (2 a right )}right)$$
Тригонометрическая часть
/ sin(a)*sin(3*a)
-1 + |2 + 2*sin(a) – —————|*sin(a)
2 /
$$left(- frac{1}{2} sin{left (a right )} sin{left (3 a right )} + 2 sin{left (a right )} + 2right) sin{left (a right )} – 1$$
Раскрыть выражение
2 / 3 2
2 2 sin (a)* – sin (a) + 3*cos (a)*sin(a)/
sin (a) – cos (a) + 2*sin(a) – ————————————–
2
$$- frac{1}{2} left(- sin^{3}{left (a right )} + 3 sin{left (a right )} cos^{2}{left (a right )}right) sin^{2}{left (a right )} + sin^{2}{left (a right )} + 2 sin{left (a right )} – cos^{2}{left (a right )}$$
