Дано
$$sin{left (- a + 180 right )} tan{left (- a + 270 right )} cos{left (a + 270 right )} + cos^{sin{left (- 2 a + 180 right )}}{left (2 a right )}$$
Подстановка условия
$$sin{left (- a + 180 right )} tan{left (- a + 270 right )} cos{left (a + 270 right )} + cos^{sin{left (- 2 a + 180 right )}}{left (2 a right )}$$
(tan(270 – (-4))*sin(180 – (-4)))*cos(270 + (-4)) + cos(2*(-4))^sin(180 – 2*(-4))
$$sin{left (- (-4) + 180 right )} tan{left (- (-4) + 270 right )} cos{left ((-4) + 270 right )} + cos^{sin{left (- 2 (-4) + 180 right )}}{left (2 (-4) right )}$$
(tan(270 – (-4))*sin(180 – (-4)))*cos(270 – 4) + cos(2*(-4))^sin(180 – 2*(-4))
$$sin{left (- -4 + 180 right )} tan{left (- -4 + 270 right )} cos{left (-4 + 270 right )} + cos^{sin{left (- -8 + 180 right )}}{left (-4 cdot 2 right )}$$
cos(8)^sin(188) + cos(266)*sin(184)*tan(274)
$$sin{left (184 right )} cos{left (266 right )} tan{left (274 right )} + cos^{sin{left (188 right )}}{left (8 right )}$$
Степени
$$sin{left (a – 180 right )} cos{left (a + 270 right )} tan{left (a – 270 right )} + cos^{- sin{left (2 a – 180 right )}}{left (2 a right )}$$
sin(-180 + 2*a)
/ 1
|——–| + cos(270 + a)*sin(-180 + a)*tan(-270 + a)
cos(2*a)/
$$left(frac{1}{cos{left (2 a right )}}right)^{sin{left (2 a – 180 right )}} + sin{left (a – 180 right )} cos{left (a + 270 right )} tan{left (a – 270 right )}$$
Численный ответ
cos(2*a)^sin(180 – 2*a) + cos(270 + a)*sin(180 – a)*tan(270 – a)
Рациональный знаменатель
$$sin{left (a – 180 right )} cos{left (a + 270 right )} tan{left (a – 270 right )} + cos^{- sin{left (2 a – 180 right )}}{left (2 a right )}$$
Объединение рациональных выражений
$$sin{left (a – 180 right )} cos{left (a + 270 right )} tan{left (a – 270 right )} + cos^{sin{left (2 left(- a + 90right) right )}}{left (2 a right )}$$
Общее упрощение
-sin(-180 + 2*a)
cos (2*a) + cos(270 + a)*sin(-180 + a)*tan(-270 + a)
$$sin{left (a – 180 right )} cos{left (a + 270 right )} tan{left (a – 270 right )} + cos^{- sin{left (2 a – 180 right )}}{left (2 a right )}$$
Общий знаменатель
-sin(-180 + 2*a)
cos (2*a) + cos(270 + a)*sin(180 – a)*tan(270 – a)
$$sin{left (- a + 180 right )} cos{left (a + 270 right )} tan{left (- a + 270 right )} + cos^{- sin{left (2 a – 180 right )}}{left (2 a right )}$$
Тригонометрическая часть
sin(180 – 2*a)
cos (2*a) + cos(270 + a)*sin(180 – a)*tan(270 – a)
$$sin{left (- a + 180 right )} cos{left (a + 270 right )} tan{left (- a + 270 right )} + cos^{sin{left (- 2 a + 180 right )}}{left (2 a right )}$$
Комбинаторика
-sin(-180 + 2*a) / sin(-180 + 2*a)
cos (2*a)*1 + cos (2*a)*cos(270 + a)*sin(-180 + a)*tan(-270 + a)/
$$left(sin{left (a – 180 right )} cos^{sin{left (2 a – 180 right )}}{left (2 a right )} cos{left (a + 270 right )} tan{left (a – 270 right )} + 1right) cos^{- sin{left (2 a – 180 right )}}{left (2 a right )}$$
Раскрыть выражение
cos(2*a)*sin(180) – cos(180)*sin(2*a)
/ 2 2 (-tan(270) + tan(a))*(cos(180)*sin(a) – cos(a)*sin(180))*(cos(270)*cos(a) – sin(270)*sin(a))
cos (a) – sin (a)/ + ——————————————————————————————–
1 + tan(270)*tan(a)
$$frac{1}{tan{left (270 right )} tan{left (a right )} + 1} left(- sin{left (270 right )} sin{left (a right )} + cos{left (270 right )} cos{left (a right )}right) left(sin{left (a right )} cos{left (180 right )} – sin{left (180 right )} cos{left (a right )}right) left(tan{left (a right )} – tan{left (270 right )}right) + left(- sin^{2}{left (a right )} + cos^{2}{left (a right )}right)^{- sin{left (2 a right )} cos{left (180 right )} + sin{left (180 right )} cos{left (2 a right )}}$$
