Докажите что:

Cos2a-sin (pi+a) sin (4pi+a) = cos^2a

4sina cosa+sin (2a-pi) = sin2a

Вначале упростим выражение: (1 - cos2a+sin2a) / (cosa - sin (2pi-a))

sin (2pi - a) = sin (-a) = - sin (a)

cos (2a) = 1 - 2sin^2 (a)

sin (2a) = 2*sin (a) * cos (a)

(1 - 1 + 2sin^2 (a) + 2sin (a) * cos (a)) / (cos (a) + sin (a)) = 2sin (a) * (sina (a) + cos (a)) / (sin (a) + cos (a)) = 2sin (a)

при sin (a) = - 1/2, 2sin (a) = 2 * (-1/2) = - 1

Ответ: - 1.