3sin^2 (x-3 п/2) - 2cos (3 п/2+х) cos (п+х) + 2sin^2 (х-п) = 2

Формулы приведения

sin (x-3pi/2) = sin (x-3pi/2+2pi) = sin (x+pi/2) = cos x

cos (x+3pi/2) = cos (x+3pi/2-2pi) = cos (x-pi/2) = cos (pi/2-x) = sin x

cos (pi+x) = - cos x

sin (x-pi) = sin (x-pi+2pi) = sin (x+pi) = - sin x

Подставляем

3cos^2 x - 2sin x * (-cos x) + 2 (-sin x) ^2 = 2sin^2 x + 2cos^2 x

Приводим подобные

cos^2 x + 2sin x*cos x = 0

cos x * (cos x + 2sin x) = 0

1) cos x = 0; x1 = pi/2 + pi*k

2) 2sin x = - cos x

tg x = - 1/2; x2 = - arctg (1/2) + pi*n