3sin^2x+1/2sin2x=2cos^2x

3sin^2 x + 1/2*2sin x*cos x - 2cos^2 x = 0
Делим все на cos^2 x
3tg^2 x + tg x - 2 = 0
(tg x + 1)(3tg x - 2) = 0
tg x = -1; x1 = pi/4 + pi*k
tg x = 2/3; x2 = arctg(2/3) + pi*n