Дано
$$frac{cos{left (x right )} cos{left (frac{180 pi}{x + 360} right )}}{- sin{left (x right )} sin{left (x + frac{90 pi}{360} right )}}$$
Подстановка условия
$$frac{cos{left (x right )} cos{left (frac{180 pi}{x + 360} right )}}{- sin{left (x right )} sin{left (x + frac{90 pi}{360} right )}}$$
(cos((180*pi)/(360 + (1/2)))*cos((1/2)))/((-sin((1/2)))*sin((90*pi)/360 + (1/2)))
$$frac{cos{left ((1/2) right )} cos{left (frac{180 pi}{(1/2) + 360} right )}}{- sin{left ((1/2) right )} sin{left ((1/2) + frac{90 pi}{360} right )}}$$
(cos((180*pi)/(360 + 1/2))*cos(1/2))/((-sin(1/2))*sin((90*pi)/360 + 1/2))
$$frac{cos{left (frac{1}{2} right )} cos{left (frac{180 pi}{frac{1}{2} + 360} right )}}{- sin{left (frac{1}{2} right )} sin{left (frac{1}{2} + frac{90 pi}{360} right )}}$$
-cos(1/2)*cos(360*pi/721)/(sin(1/2)*sin(1/2 + pi/4))
$$- frac{cos{left (frac{1}{2} right )} cos{left (frac{360 pi}{721} right )}}{sin{left (frac{1}{2} right )} sin{left (frac{1}{2} + frac{pi}{4} right )}}$$
Степени
$$- frac{cos{left (x right )} cos{left (frac{180 pi}{x + 360} right )}}{sin{left (x right )} sin{left (x + frac{pi}{4} right )}}$$
Численный ответ
-1.0*cos(x)*cos((180*pi)/(360 + x))/(sin(x)*sin((90*pi)/360 + x))
Рациональный знаменатель
$$- frac{cos{left (x right )} cos{left (frac{180 pi}{x + 360} right )}}{sin{left (x right )} sin{left (x + frac{pi}{4} right )}}$$
Объединение рациональных выражений
$$- frac{cos{left (x right )} cos{left (frac{180 pi}{x + 360} right )}}{sin{left (x right )} sin{left (frac{1}{4} left(4 x + piright) right )}}$$
Общее упрощение
/ 180*pi
-cos|——-|
360 + x/
——————
/ pi
sin|x + –|*tan(x)
4 /
$$- frac{cos{left (frac{180 pi}{x + 360} right )}}{sin{left (x + frac{pi}{4} right )} tan{left (x right )}}$$
Соберем выражение
$$- cos{left (frac{180 pi}{x + 360} right )} cot{left (x right )} csc{left (x + frac{pi}{4} right )}$$
/ 180*pi
-cos(x)*cos|——-|
360 + x/
———————
/90*pi
sin(x)*sin|—– + x|
360 /
$$- frac{cos{left (x right )} cos{left (frac{180 pi}{x + 360} right )}}{sin{left (x right )} sin{left (x + frac{90 pi}{360} right )}}$$
Общий знаменатель
/ 180*pi
-cos(x)*cos|——-|
360 + x/
———————
/ pi
sin(x)*sin|x + –|
4 /
$$- frac{cos{left (x right )} cos{left (frac{180 pi}{x + 360} right )}}{sin{left (x right )} sin{left (x + frac{pi}{4} right )}}$$
Тригонометрическая часть
/ 180*pi
-4*cos(x)*cos|——-|
360 + x/
———————–
___ / pi
/ 2 – 2*cos|2*x + –|
4 /
$$- frac{4 cos{left (x right )} cos{left (frac{180 pi}{x + 360} right )}}{- 2 cos{left (2 x + frac{pi}{4} right )} + sqrt{2}}$$
Комбинаторика
/ 180*pi
-cos(x)*cos|——-|
360 + x/
———————
/ pi
sin(x)*sin|x + –|
4 /
$$- frac{cos{left (x right )} cos{left (frac{180 pi}{x + 360} right )}}{sin{left (x right )} sin{left (x + frac{pi}{4} right )}}$$
