Дано
$$frac{cos{left (x + 90 right )} tan{left (x + 270 right )}}{cos{left (- x + 180 right )}} sin{left (- x + 90 right )}$$
Подстановка условия
$$frac{cos{left (x + 90 right )} tan{left (x + 270 right )}}{cos{left (- x + 180 right )}} sin{left (- x + 90 right )}$$
((cos(90 + (3/2))*tan(270 + (3/2)))/cos(180 – (3/2)))*sin(90 – (3/2))
$$frac{cos{left ((3/2) + 90 right )} tan{left ((3/2) + 270 right )}}{cos{left (- (3/2) + 180 right )}} sin{left (- (3/2) + 90 right )}$$
((cos(90 + 3/2)*tan(270 + 3/2))/cos(180 – 3/2))*sin(90 – 3/2)
$$frac{cos{left (frac{3}{2} + 90 right )} tan{left (frac{3}{2} + 270 right )}}{cos{left (- frac{3}{2} + 180 right )}} sin{left (- frac{3}{2} + 90 right )}$$
cos(183/2)*sin(177/2)*tan(543/2)/cos(357/2)
$$frac{sin{left (frac{177}{2} right )} cos{left (frac{183}{2} right )}}{cos{left (frac{357}{2} right )}} tan{left (frac{543}{2} right )}$$
Степени
$$- frac{sin{left (x – 90 right )} cos{left (x + 90 right )}}{cos{left (x – 180 right )}} tan{left (x + 270 right )}$$
Численный ответ
cos(90 + x)*sin(90 – x)*tan(270 + x)/cos(180 – x)
Рациональный знаменатель
$$- frac{sin{left (x – 90 right )} cos{left (x + 90 right )}}{cos{left (x – 180 right )}} tan{left (x + 270 right )}$$
Объединение рациональных выражений
$$- frac{sin{left (x – 90 right )} cos{left (x + 90 right )}}{cos{left (x – 180 right )}} tan{left (x + 270 right )}$$
Общее упрощение
-cos(90 + x)*sin(-90 + x)*tan(270 + x)
—————————————
cos(-180 + x)
$$- frac{sin{left (x – 90 right )} cos{left (x + 90 right )}}{cos{left (x – 180 right )}} tan{left (x + 270 right )}$$
Соберем выражение
$$- left(frac{1}{2} sin{left (2 x right )} – frac{1}{2} sin{left (180 right )}right) tan{left (x + 270 right )} sec{left (x – 180 right )}$$
cos(90 + x)*sin(90 – x)*tan(270 + x)
————————————
cos(180 – x)
$$frac{sin{left (- x + 90 right )} cos{left (x + 90 right )}}{cos{left (- x + 180 right )}} tan{left (x + 270 right )}$$
Общий знаменатель
cos(90 + x)*sin(90 – x)*tan(270 + x)
————————————
cos(180 – x)
$$frac{sin{left (- x + 90 right )} cos{left (x + 90 right )}}{cos{left (- x + 180 right )}} tan{left (x + 270 right )}$$
Тригонометрическая часть
cos(90 + x)*sin(90 – x)*tan(270 + x)
————————————
cos(-180 + x)
$$frac{cos{left (x + 90 right )} tan{left (x + 270 right )}}{cos{left (x – 180 right )}} sin{left (- x + 90 right )}$$
Комбинаторика
-cos(90 + x)*sin(-90 + x)*tan(270 + x)
—————————————
cos(-180 + x)
$$- frac{sin{left (x – 90 right )} cos{left (x + 90 right )}}{cos{left (x – 180 right )}} tan{left (x + 270 right )}$$
Раскрыть выражение
-(cos(90)*cos(x) – sin(90)*sin(x))*(cos(90)*sin(x) – cos(x)*sin(90))*(tan(270) + tan(x))
—————————————————————————————–
(1 – tan(270)*tan(x))*(cos(180)*cos(x) + sin(180)*sin(x))
$$- frac{left(- sin{left (90 right )} sin{left (x right )} + cos{left (90 right )} cos{left (x right )}right) left(sin{left (x right )} cos{left (90 right )} – sin{left (90 right )} cos{left (x right )}right) left(tan{left (x right )} + tan{left (270 right )}right)}{left(sin{left (180 right )} sin{left (x right )} + cos{left (180 right )} cos{left (x right )}right) left(- tan{left (270 right )} tan{left (x right )} + 1right)}$$
