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