Дано
$$frac{sin{left (a right )} + 1 – cos{left (2 a right )} – sin{left (3 a right )}}{2 sin^{2}{left (a right )} + sin{left (a right )} – 1}$$
Подстановка условия
$$frac{sin{left (a right )} + 1 – cos{left (2 a right )} – sin{left (3 a right )}}{2 sin^{2}{left (a right )} + sin{left (a right )} – 1}$$
(1 + sin((1)) – cos(2*(1)) – sin(3*(1)))/(2*sin((1))^2 + sin((1)) – 1)
$$frac{sin{left ((1) right )} + 1 – cos{left (2 (1) right )} – sin{left (3 (1) right )}}{2 sin^{2}{left ((1) right )} + sin{left ((1) right )} – 1}$$
(1 + sin(1) – cos(2) – sin(3))/(2*sin(1)^2 + sin(1) – 1)
$$frac{- sin{left (3 right )} + – cos{left (2 right )} + sin{left (1 right )} + 1}{-1 + sin{left (1 right )} + 2 sin^{2}{left (1 right )}}$$
(1 – cos(2) – sin(3) + sin(1))/(-1 + 2*sin(1)^2 + sin(1))
$$frac{- sin{left (3 right )} – cos{left (2 right )} + sin{left (1 right )} + 1}{-1 + sin{left (1 right )} + 2 sin^{2}{left (1 right )}}$$
Степени
$$frac{sin{left (a right )} – sin{left (3 a right )} – cos{left (2 a right )} + 1}{2 sin^{2}{left (a right )} + sin{left (a right )} – 1}$$
Численный ответ
(1.0 – cos(2*a) – sin(3*a) + sin(a))/(-1.0 + 2.0*sin(a)^2 + sin(a))
Рациональный знаменатель
$$frac{sin{left (a right )} – sin{left (3 a right )} – cos{left (2 a right )} + 1}{2 sin^{2}{left (a right )} + sin{left (a right )} – 1}$$
Объединение рациональных выражений
$$frac{sin{left (a right )} – sin{left (3 a right )} – cos{left (2 a right )} + 1}{left(2 sin{left (a right )} + 1right) sin{left (a right )} – 1}$$
Общее упрощение
2
-sin(3*a) + 2*sin (a) + sin(a)
——————————
-cos(2*a) + sin(a)
$$frac{2 sin^{2}{left (a right )} + sin{left (a right )} – sin{left (3 a right )}}{sin{left (a right )} – cos{left (2 a right )}}$$
Соберем выражение
$$- frac{sin{left (a right )}}{- sin{left (a right )} + cos{left (2 a right )}} + frac{sin{left (3 a right )}}{- sin{left (a right )} + cos{left (2 a right )}} + frac{cos{left (2 a right )}}{- sin{left (a right )} + cos{left (2 a right )}} – frac{1}{- sin{left (a right )} + cos{left (2 a right )}}$$
1 – cos(2*a) – sin(3*a) + sin(a)
——————————–
2
-1 + 2*sin (a) + sin(a)
$$frac{sin{left (a right )} – sin{left (3 a right )} – cos{left (2 a right )} + 1}{2 sin^{2}{left (a right )} + sin{left (a right )} – 1}$$
Общий знаменатель
-(-1 – sin(a) + cos(2*a) + sin(3*a))
————————————-
2
-1 + 2*sin (a) + sin(a)
$$- frac{- sin{left (a right )} + sin{left (3 a right )} + cos{left (2 a right )} – 1}{2 sin^{2}{left (a right )} + sin{left (a right )} – 1}$$
Тригонометрическая часть
2
-sin(3*a) + 2*sin (a) + sin(a)
——————————
-cos(2*a) + sin(a)
$$frac{2 sin^{2}{left (a right )} + sin{left (a right )} – sin{left (3 a right )}}{sin{left (a right )} – cos{left (2 a right )}}$$
Комбинаторика
-(-1 – sin(a) + cos(2*a) + sin(3*a))
————————————-
(1 + sin(a))*(-1 + 2*sin(a))
$$- frac{- sin{left (a right )} + sin{left (3 a right )} + cos{left (2 a right )} – 1}{left(sin{left (a right )} + 1right) left(2 sin{left (a right )} – 1right)}$$
Раскрыть выражение
2 3 2 2
1 + sin (a) + sin (a) – cos (a) – 3*cos (a)*sin(a) + sin(a)
———————————————————–
2
-1 + 2*sin (a) + sin(a)
$$frac{1}{2 sin^{2}{left (a right )} + sin{left (a right )} – 1} left(sin^{3}{left (a right )} + sin^{2}{left (a right )} – 3 sin{left (a right )} cos^{2}{left (a right )} + sin{left (a right )} – cos^{2}{left (a right )} + 1right)$$
