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

2-3sin (3π/2+x) + cos² (x/2) - sin² (x/2) = 0

2+3sinx+cos² (x/2) - sin² (x/2) = 0

2sin² (x/2) + 2cos² (x/2) + 6sin (x/2) cos (x/2) + cos² (x/2) - sin² (x/2) = 0

sin² (x/2) + 6sin (x/2) cos (x/2) + 3cos² (x/2) = 0/cos² (x/2)

tg² (x/2) + 6tg (x/2) + 3=0

tg (x/2) = a

a2+6a+3=0

D=36-12=24

a1 = (-6-2√6) / 2=-3-√6⇒tg (x/2) = - 3-√6⇒x/2=-arctg (3+√6) + πn⇒x=-1arctg (3+√6) + 2πn

a2=-3+√6⇒tg (x/2) = √6-3⇒x/2=arctg (√6-3) + πn⇒x=2arctg (√6-3) + 2πn