Дано
$$frac{1}{sin{left (2 x right )}} left(sin{left (frac{3 p}{2} + 2 x right )} + 1 – sin^{2}{left (x right )}right) sin{left (frac{p}{2} + x right )} + sin{left (x right )} cos{left (p – 2 x right )}$$
Подстановка условия
$$frac{1}{sin{left (2 x right )}} left(sin{left (frac{3 p}{2} + 2 x right )} + 1 – sin^{2}{left (x right )}right) sin{left (frac{p}{2} + x right )} + sin{left (x right )} cos{left (p – 2 x right )}$$
((1 + sin((3*(-1/4))/2 + 2*x) – sin(x)^2)/sin(2*x))*sin((-1/4)/2 + x) + sin(x)*cos((-1/4) – 2*x)
$$frac{1}{sin{left (2 x right )}} left(sin{left (frac{3 (-1/4)}{2} + 2 x right )} + 1 – sin^{2}{left (x right )}right) sin{left (frac{(-1/4)}{2} + x right )} + sin{left (x right )} cos{left ((-1/4) – 2 x right )}$$
((1 + sin((3*(-1)/4)/2 + 2*x) – sin(x)^2)/sin(2*x))*sin(-1/8 + x) + sin(x)*cos(-1/4 – 2*x)
$$frac{1}{sin{left (2 x right )}} left(sin{left (2 x + frac{- frac{3}{4}}{2} 1 right )} + 1 – sin^{2}{left (x right )}right) sin{left (x – frac{1}{8} right )} + sin{left (x right )} cos{left (- 2 x – frac{1}{4} right )}$$
cos(1/4 + 2*x)*sin(x) + (1 – sin(x)^2 + sin(-3/8 + 2*x))*sin(-1/8 + x)/sin(2*x)
$$frac{sin{left (x – frac{1}{8} right )}}{sin{left (2 x right )}} left(- sin^{2}{left (x right )} + sin{left (2 x – frac{3}{8} right )} + 1right) + sin{left (x right )} cos{left (2 x + frac{1}{4} right )}$$
Степени
$$frac{sin{left (frac{p}{2} + x right )}}{sin{left (2 x right )}} left(- sin^{2}{left (x right )} + sin{left (frac{3 p}{2} + 2 x right )} + 1right) + sin{left (x right )} cos{left (p – 2 x right )}$$
Численный ответ
cos(p – 2*x)*sin(x) + (1.0 – sin(x)^2 + sin((3*p)/2 + 2*x))*sin(p/2 + x)/sin(2*x)
Рациональный знаменатель
$$frac{1}{sin{left (2 x right )}} left(- sin^{2}{left (x right )} sin{left (frac{p}{2} + x right )} + sin{left (x right )} sin{left (2 x right )} cos{left (p – 2 x right )} + sin{left (frac{p}{2} + x right )} sin{left (frac{3 p}{2} + 2 x right )} + sin{left (frac{p}{2} + x right )}right)$$
Объединение рациональных выражений
$$frac{1}{sin{left (2 x right )}} left(left(- sin^{2}{left (x right )} + sin{left (frac{1}{2} left(3 p + 4 xright) right )} + 1right) sin{left (frac{1}{2} left(p + 2 xright) right )} + sin{left (x right )} sin{left (2 x right )} cos{left (p – 2 x right )}right)$$
Общее упрощение
/ 2 / 3*p / p
|1 – sin (x) + sin|2*x + —||*sin|x + -| + cos(p – 2*x)*sin(x)*sin(2*x)
2 // 2/
————————————————————————
sin(2*x)
$$frac{1}{sin{left (2 x right )}} left(left(- sin^{2}{left (x right )} + sin{left (frac{3 p}{2} + 2 x right )} + 1right) sin{left (frac{p}{2} + x right )} + sin{left (x right )} sin{left (2 x right )} cos{left (p – 2 x right )}right)$$
Соберем выражение
$$left(frac{1}{4} sin{left (frac{p}{2} – x right )} + frac{1}{2} sin{left (frac{p}{2} + x right )} + frac{1}{4} sin{left (frac{p}{2} + 3 x right )} + frac{1}{2} cos{left (p + x right )} – frac{1}{2} cos{left (2 p + 3 x right )}right) csc{left (2 x right )} – frac{1}{2} sin{left (p – 3 x right )} + frac{1}{2} sin{left (p – x right )}$$
Комбинаторика
/ p / 3*p 2 / p / p
sin|x + -|*sin|2*x + —| – sin (x)*sin|x + -| + cos(p – 2*x)*sin(x)*sin(2*x) + sin|x + -|
2/ 2 / 2/ 2/
——————————————————————————————
sin(2*x)
$$frac{1}{sin{left (2 x right )}} left(- sin^{2}{left (x right )} sin{left (frac{p}{2} + x right )} + sin{left (x right )} sin{left (2 x right )} cos{left (p – 2 x right )} + sin{left (frac{p}{2} + x right )} sin{left (frac{3 p}{2} + 2 x right )} + sin{left (frac{p}{2} + x right )}right)$$
Общий знаменатель
/ p / 3*p 2 / p / p
sin|x + -|*sin|2*x + —| – sin (x)*sin|x + -| + sin|x + -|
2/ 2 / 2/ 2/
———————————————————– + cos(p – 2*x)*sin(x)
sin(2*x)
$$frac{1}{sin{left (2 x right )}} left(- sin^{2}{left (x right )} sin{left (frac{p}{2} + x right )} + sin{left (frac{p}{2} + x right )} sin{left (frac{3 p}{2} + 2 x right )} + sin{left (frac{p}{2} + x right )}right) + sin{left (x right )} cos{left (p – 2 x right )}$$
Тригонометрическая часть
/ 2 / 3*p /p
|1 – sin (x) + sin|2*x + —||*sin|- + x|
2 // 2 /
cos(p – 2*x)*sin(x) + —————————————–
sin(2*x)
$$frac{sin{left (frac{p}{2} + x right )}}{sin{left (2 x right )}} left(- sin^{2}{left (x right )} + sin{left (frac{3 p}{2} + 2 x right )} + 1right) + sin{left (x right )} cos{left (p – 2 x right )}$$
Раскрыть выражение
/ /p /p / 2 /3*p /3*p
|cos(x)*sin|-| + cos|-|*sin(x)|*|1 – sin (x) + cos(2*x)*sin|—| + cos|—|*sin(2*x)|
2/ 2/ / 2 / 2 / /
(cos(p)*cos(2*x) + sin(p)*sin(2*x))*sin(x) + ————————————————————————————-
2*cos(x)*sin(x)
$$frac{1}{2 sin{left (x right )} cos{left (x right )}} left(sin{left (frac{p}{2} right )} cos{left (x right )} + sin{left (x right )} cos{left (frac{p}{2} right )}right) left(sin{left (frac{3 p}{2} right )} cos{left (2 x right )} – sin^{2}{left (x right )} + sin{left (2 x right )} cos{left (frac{3 p}{2} right )} + 1right) + left(sin{left (p right )} sin{left (2 x right )} + cos{left (p right )} cos{left (2 x right )}right) sin{left (x right )}$$
