решите 3+2sin3xsinx=3cos2x

3 + 2sin3xsinx = 3cos2x
2sin3xsinx = 3cos2x - 3
cos(3x - x) - cos(3x + x) = 3cos2x - 3
cos2x - cos4x = 3cos2x - 3 
-cos4x = 2cos2x - 3
-(2cos2x - 1) = 2cos2x - 3
-2cos2x - 2cos2x + 1 + 3 = 0
cos2x + cos2x - 2 = 0
Пусть t = cos2x, t  [-1; 1].
t + t - 2 = 0
t + t = -1
tt = -2
t = -2 - не подходит; t = 1
Оборотная замена:
cos2x = 1
2x = 2n, n  Z 
x = n, n  Z 
Ответ: x = n, n  Z.