Дано
$$- cos{left (a + 2 pi right )} + frac{cos{left (2 a right )}}{- sin{left (a right )} + cos{left (a right )}}$$
Подстановка условия
$$- cos{left (a + 2 pi right )} + frac{cos{left (2 a right )}}{- sin{left (a right )} + cos{left (a right )}}$$
-cos(2*pi + (2)) + cos(2*(2))/(cos((2)) – sin((2)))
$$- cos{left ((2) + 2 pi right )} + frac{cos{left (2 (2) right )}}{- sin{left ((2) right )} + cos{left ((2) right )}}$$
-cos(2*pi + 2) + cos(2*2)/(cos(2) – sin(2))
$$- cos{left (2 + 2 pi right )} + frac{cos{left (2 cdot 2 right )}}{- sin{left (2 right )} + cos{left (2 right )}}$$
-cos(2) + cos(4)/(-sin(2) + cos(2))
$$- cos{left (2 right )} + frac{cos{left (4 right )}}{- sin{left (2 right )} + cos{left (2 right )}}$$
Степени
$$- cos{left (a right )} + frac{cos{left (2 a right )}}{- sin{left (a right )} + cos{left (a right )}}$$
Численный ответ
-cos(2*pi + a) + cos(2*a)/(-sin(a) + cos(a))
Рациональный знаменатель
$$frac{1}{sin{left (a right )} – cos{left (a right )}} left(- sin{left (a right )} cos{left (a right )} + cos^{2}{left (a right )} – cos{left (2 a right )}right)$$
Объединение рациональных выражений
$$frac{1}{- sin{left (a right )} + cos{left (a right )}} left(- left(- sin{left (a right )} + cos{left (a right )}right) cos{left (a right )} + cos{left (2 a right )}right)$$
Общее упрощение
$$sin{left (a right )}$$
Соберем выражение
$$- cos{left (a right )} – frac{cos{left (2 a right )}}{sin{left (a right )} – cos{left (a right )}}$$
Общий знаменатель
cos(2*a)
-cos(a) + —————-
-sin(a) + cos(a)
$$- cos{left (a right )} + frac{cos{left (2 a right )}}{- sin{left (a right )} + cos{left (a right )}}$$
Тригонометрическая часть
___
/ 2 *cos(2*a)
-cos(a) + ————–
/ pi
2*cos|a + –|
4 /
$$- cos{left (a right )} + frac{sqrt{2} cos{left (2 a right )}}{2 cos{left (a + frac{pi}{4} right )}}$$
Комбинаторика
2
– cos (a) + cos(a)*sin(a) + cos(2*a)
————————————
-sin(a) + cos(a)
$$frac{sin{left (a right )} cos{left (a right )} – cos^{2}{left (a right )} + cos{left (2 a right )}}{- sin{left (a right )} + cos{left (a right )}}$$
Раскрыть выражение
2 2
cos (a) – sin (a)
-cos(a) + —————–
-sin(a) + cos(a)
$$- cos{left (a right )} + frac{- sin^{2}{left (a right )} + cos^{2}{left (a right )}}{- sin{left (a right )} + cos{left (a right )}}$$