Дано
$$frac{sin{left (frac{3 p}{2} + 2 x right )} + 1 – sin^{2}{left (x right )}}{sin{left (x right )} cos{left (p – 2 x right )} + sin{left (2 x right )} sin{left (frac{p}{2} + x right )}}$$
Подстановка условия
$$frac{sin{left (frac{3 p}{2} + 2 x right )} + 1 – sin^{2}{left (x right )}}{sin{left (x right )} cos{left (p – 2 x right )} + sin{left (2 x right )} sin{left (frac{p}{2} + x right )}}$$
(1 + sin((3*(3))/2 + 2*x) – sin(x)^2)/(sin(2*x)*sin((3)/2 + x) + sin(x)*cos((3) – 2*x))
$$frac{sin{left (frac{3 (3)}{2} + 2 x right )} + 1 – sin^{2}{left (x right )}}{sin{left (x right )} cos{left ((3) – 2 x right )} + sin{left (2 x right )} sin{left (frac{(3)}{2} + x right )}}$$
(1 + sin((3*3)/2 + 2*x) – sin(x)^2)/(sin(2*x)*sin(3/2 + x) + sin(x)*cos(3 – 2*x))
$$frac{sin{left (2 x + frac{9}{2} 1 right )} + 1 – sin^{2}{left (x right )}}{sin{left (x right )} cos{left (- 2 x + 3 right )} + sin{left (2 x right )} sin{left (x + frac{3}{2} right )}}$$
(1 – sin(x)^2 + sin(9/2 + 2*x))/(cos(-3 + 2*x)*sin(x) + sin(2*x)*sin(3/2 + x))
$$frac{- sin^{2}{left (x right )} + sin{left (2 x + frac{9}{2} right )} + 1}{sin{left (x right )} cos{left (2 x – 3 right )} + sin{left (2 x right )} sin{left (x + frac{3}{2} right )}}$$
Степени
$$frac{- sin^{2}{left (x right )} + sin{left (frac{3 p}{2} + 2 x right )} + 1}{sin{left (x right )} cos{left (p – 2 x right )} + sin{left (2 x right )} sin{left (frac{p}{2} + x right )}}$$
Численный ответ
(1.0 – sin(x)^2 + sin((3*p)/2 + 2*x))/(cos(p – 2*x)*sin(x) + sin(2*x)*sin(p/2 + x))
Рациональный знаменатель
$$frac{- sin^{2}{left (x right )} + sin{left (frac{3 p}{2} + 2 x right )} + 1}{sin{left (x right )} cos{left (p – 2 x right )} + sin{left (2 x right )} sin{left (frac{p}{2} + x right )}}$$
Объединение рациональных выражений
$$frac{- sin^{2}{left (x right )} + sin{left (frac{1}{2} left(3 p + 4 xright) right )} + 1}{sin{left (x right )} cos{left (p – 2 x right )} + sin{left (2 x right )} sin{left (frac{1}{2} left(p + 2 xright) right )}}$$
Общее упрощение
2 / 3*p
1 – sin (x) + sin|2*x + —|
2 /
—————————————–
/ p
cos(p – 2*x)*sin(x) + sin(2*x)*sin|x + -|
2/
$$frac{- sin^{2}{left (x right )} + sin{left (frac{3 p}{2} + 2 x right )} + 1}{sin{left (x right )} cos{left (p – 2 x right )} + sin{left (2 x right )} sin{left (frac{p}{2} + x right )}}$$
Соберем выражение
$$- frac{2 sin{left (frac{3 p}{2} + 2 x right )}}{sin{left (p – 3 x right )} – sin{left (p – x right )} – cos{left (frac{p}{2} – x right )} + cos{left (frac{p}{2} + 3 x right )}} – frac{cos{left (2 x right )}}{sin{left (p – 3 x right )} – sin{left (p – x right )} – cos{left (frac{p}{2} – x right )} + cos{left (frac{p}{2} + 3 x right )}} – frac{1}{sin{left (p – 3 x right )} – sin{left (p – x right )} – cos{left (frac{p}{2} – x right )} + cos{left (frac{p}{2} + 3 x right )}}$$
2 /3*p
1 – sin (x) + sin|— + 2*x|
2 /
—————————————–
/p
sin(x)*cos(p – 2*x) + sin(2*x)*sin|- + x|
2 /
$$frac{- sin^{2}{left (x right )} + sin{left (frac{3 p}{2} + 2 x right )} + 1}{sin{left (x right )} cos{left (p – 2 x right )} + sin{left (2 x right )} sin{left (frac{p}{2} + x right )}}$$
Общий знаменатель
2 / 3*p
1 – sin (x) + sin|2*x + —|
2 /
—————————————–
/ p
cos(p – 2*x)*sin(x) + sin(2*x)*sin|x + -|
2/
$$frac{- sin^{2}{left (x right )} + sin{left (frac{3 p}{2} + 2 x right )} + 1}{sin{left (x right )} cos{left (p – 2 x right )} + sin{left (2 x right )} sin{left (frac{p}{2} + x right )}}$$
Тригонометрическая часть
2 / 3*p
1 – sin (x) + sin|2*x + —|
2 /
—————————————–
/p
cos(p – 2*x)*sin(x) + sin(2*x)*sin|- + x|
2 /
$$frac{- sin^{2}{left (x right )} + sin{left (frac{3 p}{2} + 2 x right )} + 1}{sin{left (x right )} cos{left (p – 2 x right )} + sin{left (2 x right )} sin{left (frac{p}{2} + x right )}}$$
Комбинаторика
2 / 3*p
1 – sin (x) + sin|2*x + —|
2 /
—————————————–
/ p
cos(p – 2*x)*sin(x) + sin(2*x)*sin|x + -|
2/
$$frac{- sin^{2}{left (x right )} + sin{left (frac{3 p}{2} + 2 x right )} + 1}{sin{left (x right )} cos{left (p – 2 x right )} + sin{left (2 x right )} sin{left (frac{p}{2} + x right )}}$$
Раскрыть выражение
2 /3*p /3*p
1 – sin (x) + cos(2*x)*sin|—| + cos|—|*sin(2*x)
2 / 2 /
——————————————————————————————–
/ /p /p
(cos(p)*cos(2*x) + sin(p)*sin(2*x))*sin(x) + 2*|cos(x)*sin|-| + cos|-|*sin(x)|*cos(x)*sin(x)
2/ 2/ /
$$frac{sin{left (frac{3 p}{2} right )} cos{left (2 x right )} – sin^{2}{left (x right )} + sin{left (2 x right )} cos{left (frac{3 p}{2} right )} + 1}{2 left(sin{left (frac{p}{2} right )} cos{left (x right )} + sin{left (x right )} cos{left (frac{p}{2} right )}right) sin{left (x right )} cos{left (x right )} + left(sin{left (p right )} sin{left (2 x right )} + cos{left (p right )} cos{left (2 x right )}right) sin{left (x right )}}$$
