1) cosx + 3sin(x/2) = -1
1-2sin²(x/2)+3sin(x/2)+1=0
sinx/2=a
2a²-3a-2=0
D=9+16=25
a1=(3-5)/4=-1/2⇒sinx=-1/2⇒x=-π/6+2πk U x=-5π/6+2πk,k∈z
2) cos^2(x+п/4) = 0,5
(1+cos(2x+π/2))/2=1/2
1+cos(2x+π/2)=1
cos(2x+π/2)=0
-sin2x=0
2x=πk
x=πk/2,k∈z
3) 2sin^2(x/2) + 3sinx + 2 = 0
1-cosx+3sinx+2=0
3sinx-cosx+3=0
6sinx/2*cosx/2-cos²x/2+sin²x/2+3cos²x/2+3sin²x/2=0
4sin²x/2+6sinx/2*cosx/2+2cos²x/2=0/cos²x
4tg²x/2+6tgx/2+2=0
2tg²x/2+3tgx/2+1=0
tgx/2=a
2a²+3a+1=0
D=9-8=1
a1=(-3-1)/4=-1⇒tgx/2=-1⇒x/2=-π/4+πk⇒x=-π/22πk,k∈z
a2=(-3+4)/4=1/4⇒tgx/2=1/4⇒⇒x/2=arctg1/4+πk⇒x=2arctg1/4+2πk,k∈z