Дано
$$frac{frac{1}{tan{left (- x + 270 right )}}}{cos{left (x + 270 right )}} left(sin^{2}{left (x + 90 right )} + sin^{2}{left (x + 180 right )}right)$$
Подстановка условия
$$frac{frac{1}{tan{left (- x + 270 right )}}}{cos{left (x + 270 right )}} left(sin^{2}{left (x + 90 right )} + sin^{2}{left (x + 180 right )}right)$$
((sin(180 + (1/3))^2 + sin(90 + (1/3))^2)/tan(270 – (1/3)))/cos(270 + (1/3))
$$frac{frac{1}{tan{left (- (1/3) + 270 right )}}}{cos{left ((1/3) + 270 right )}} left(sin^{2}{left ((1/3) + 90 right )} + sin^{2}{left ((1/3) + 180 right )}right)$$
((sin(180 + 1/3)^2 + sin(90 + 1/3)^2)/tan(270 – 1/3))/cos(270 + 1/3)
$$frac{frac{1}{tan{left (- frac{1}{3} + 270 right )}}}{cos{left (frac{1}{3} + 270 right )}} left(sin^{2}{left (frac{1}{3} + 90 right )} + sin^{2}{left (frac{1}{3} + 180 right )}right)$$
(sin(271/3)^2 + sin(541/3)^2)/(cos(811/3)*tan(809/3))
$$frac{sin^{2}{left (frac{271}{3} right )} + sin^{2}{left (frac{541}{3} right )}}{cos{left (frac{811}{3} right )} tan{left (frac{809}{3} right )}}$$
Степени
$$frac{- sin^{2}{left (x + 90 right )} – sin^{2}{left (x + 180 right )}}{cos{left (x + 270 right )} tan{left (x – 270 right )}}$$
/ 2 2
-sin (90 + x) + sin (180 + x)/
——————————–
cos(270 + x)*tan(-270 + x)
$$- frac{sin^{2}{left (x + 90 right )} + sin^{2}{left (x + 180 right )}}{cos{left (x + 270 right )} tan{left (x – 270 right )}}$$
Численный ответ
(sin(90 + x)^2 + sin(180 + x)^2)/(cos(270 + x)*tan(270 – x))
Рациональный знаменатель
$$frac{- sin^{2}{left (x + 90 right )} – sin^{2}{left (x + 180 right )}}{cos{left (x + 270 right )} tan{left (x – 270 right )}}$$
Объединение рациональных выражений
$$- frac{sin^{2}{left (x + 90 right )} + sin^{2}{left (x + 180 right )}}{cos{left (x + 270 right )} tan{left (x – 270 right )}}$$
Общее упрощение
/ 2 2
-sin (90 + x) + sin (180 + x)/
——————————–
cos(270 + x)*tan(-270 + x)
$$- frac{sin^{2}{left (x + 90 right )} + sin^{2}{left (x + 180 right )}}{cos{left (x + 270 right )} tan{left (x – 270 right )}}$$
Соберем выражение
$$- left(- frac{1}{2} cos{left (2 x + 180 right )} – frac{1}{2} cos{left (2 x + 360 right )} + 1right) cot{left (x – 270 right )} sec{left (x + 270 right )}$$
2 2
sin (90 + x) + sin (180 + x)
—————————-
cos(270 + x)*tan(270 – x)
$$frac{sin^{2}{left (x + 90 right )} + sin^{2}{left (x + 180 right )}}{cos{left (x + 270 right )} tan{left (- x + 270 right )}}$$
Общий знаменатель
2 2
sin (90 + x) + sin (180 + x)
—————————-
cos(270 + x)*tan(270 – x)
$$frac{sin^{2}{left (x + 90 right )} + sin^{2}{left (x + 180 right )}}{cos{left (x + 270 right )} tan{left (- x + 270 right )}}$$
Тригонометрическая часть
2 2
sin (180 + x) + sin (90 + x)
—————————-
cos(270 + x)*tan(270 – x)
$$frac{sin^{2}{left (x + 90 right )} + sin^{2}{left (x + 180 right )}}{cos{left (x + 270 right )} tan{left (- x + 270 right )}}$$
Комбинаторика
/ 2 2
-sin (90 + x) + sin (180 + x)/
——————————–
cos(270 + x)*tan(-270 + x)
$$- frac{sin^{2}{left (x + 90 right )} + sin^{2}{left (x + 180 right )}}{cos{left (x + 270 right )} tan{left (x – 270 right )}}$$
Раскрыть выражение
/ 2 2
-(1 + tan(270)*tan(x))*(cos(90)*sin(x) + cos(x)*sin(90)) + (cos(180)*sin(x) + cos(x)*sin(180)) /
—————————————————————————————————
(-tan(270) + tan(x))*(cos(270)*cos(x) – sin(270)*sin(x))
$$- frac{left(tan{left (270 right )} tan{left (x right )} + 1right) left(left(sin{left (x right )} cos{left (90 right )} + sin{left (90 right )} cos{left (x right )}right)^{2} + left(sin{left (x right )} cos{left (180 right )} + sin{left (180 right )} cos{left (x right )}right)^{2}right)}{left(- sin{left (270 right )} sin{left (x right )} + cos{left (270 right )} cos{left (x right )}right) left(tan{left (x right )} – tan{left (270 right )}right)}$$
