Дано
$$sin{left (- a + 180 right )} sin{left (a + 90 right )} left(tan{left (- a + 270 right )} + tan{left (a + 180 right )}right)$$
Подстановка условия
$$sin{left (- a + 180 right )} sin{left (a + 90 right )} left(tan{left (- a + 270 right )} + tan{left (a + 180 right )}right)$$
(sin(90 + (3))*sin(180 – (3)))*(tan(180 + (3)) + tan(270 – (3)))
$$sin{left (- (3) + 180 right )} sin{left ((3) + 90 right )} left(tan{left (- (3) + 270 right )} + tan{left ((3) + 180 right )}right)$$
(sin(90 + 3)*sin(180 – 3))*(tan(180 + 3) + tan(270 – 3))
$$sin{left (3 + 90 right )} sin{left (- 3 + 180 right )} left(tan{left (- 3 + 270 right )} + tan{left (3 + 180 right )}right)$$
(tan(183) + tan(267))*sin(93)*sin(177)
$$left(tan{left (267 right )} + tan{left (183 right )}right) sin{left (93 right )} sin{left (177 right )}$$
Степени
$$- left(- tan{left (a – 270 right )} + tan{left (a + 180 right )}right) sin{left (a – 180 right )} sin{left (a + 90 right )}$$
Численный ответ
(tan(180 + a) + tan(270 – a))*sin(90 + a)*sin(180 – a)
Рациональный знаменатель
$$left(tan{left (a – 270 right )} – tan{left (a + 180 right )}right) sin{left (a – 180 right )} sin{left (a + 90 right )}$$
Объединение рациональных выражений
$$- left(- tan{left (a – 270 right )} + tan{left (a + 180 right )}right) sin{left (a – 180 right )} sin{left (a + 90 right )}$$
Общее упрощение
(-tan(180 + a) + tan(-270 + a))*sin(-180 + a)*sin(90 + a)
$$left(tan{left (a – 270 right )} – tan{left (a + 180 right )}right) sin{left (a – 180 right )} sin{left (a + 90 right )}$$
Соберем выражение
$$- frac{1}{2} cos{left (2 a – 90 right )} tan{left (a – 270 right )} + frac{1}{2} cos{left (2 a – 90 right )} tan{left (a + 180 right )} + frac{1}{2} cos{left (270 right )} tan{left (a – 270 right )} – frac{1}{2} cos{left (270 right )} tan{left (a + 180 right )}$$
(tan(180 + a) + tan(270 – a))*sin(90 + a)*sin(180 – a)
$$left(tan{left (- a + 270 right )} + tan{left (a + 180 right )}right) sin{left (- a + 180 right )} sin{left (a + 90 right )}$$
Общий знаменатель
sin(90 + a)*sin(180 – a)*tan(180 + a) + sin(90 + a)*sin(180 – a)*tan(270 – a)
$$sin{left (- a + 180 right )} sin{left (a + 90 right )} tan{left (- a + 270 right )} + sin{left (- a + 180 right )} sin{left (a + 90 right )} tan{left (a + 180 right )}$$
Тригонометрическая часть
(tan(180 + a) + tan(270 – a))*sin(90 + a)*sin(180 – a)
$$left(tan{left (- a + 270 right )} + tan{left (a + 180 right )}right) sin{left (- a + 180 right )} sin{left (a + 90 right )}$$
Комбинаторика
-(-tan(-270 + a) + tan(180 + a))*sin(-180 + a)*sin(90 + a)
$$- left(- tan{left (a – 270 right )} + tan{left (a + 180 right )}right) sin{left (a – 180 right )} sin{left (a + 90 right )}$$
Раскрыть выражение
/ tan(180) + tan(a) -tan(270) + tan(a)
|——————- – ——————-|*(cos(180)*sin(a) – cos(a)*sin(180))*(-cos(90)*sin(a) – cos(a)*sin(90))
1 – tan(180)*tan(a) 1 + tan(270)*tan(a)/
$$left(- frac{tan{left (a right )} – tan{left (270 right )}}{tan{left (270 right )} tan{left (a right )} + 1} + frac{tan{left (a right )} + tan{left (180 right )}}{- tan{left (180 right )} tan{left (a right )} + 1}right) left(- sin{left (a right )} cos{left (90 right )} – sin{left (90 right )} cos{left (a right )}right) left(sin{left (a right )} cos{left (180 right )} – sin{left (180 right )} cos{left (a right )}right)$$
