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