Уравнения во вложении...

Решение
1.  Sin2xcosx+cos2xsinx= 3/2
sin(2x + x) = 3/2
sin3x = 3/2
3x = (-1)^x arcsin(3/2) + n, n Z
3x = (-1)^n *(/3) + n, nZ
x = (-1)^n *(/9) + n/3, nZ
 
2.  Cosx+cosx= 1/2 - sinx
cosx = 1/2 - 1
cosx = - 1/2
x = (+ -)arccos(-1/2) + 2n, n  Z
x = (+ -)*( - arccos(1/2)) + 2n, n  Z
x = (+ -)*( - /3) + 2n, nZ
x = (+ -)*(2/3) + 2n, nZ

3. Sin3xcosx-cos3xsinx = 3/2
sin(3x - x) = 3/2
sin2x = 3/2
2x = (-1)^n arcsin(3/2) + k, k  Z
2x = (-1)^n * (/3) + k, k  Z
x = (-1)^n * (/6) + k/2, k  Z