1)8sin(x/2)cos(x/2)=5cos²(x/2)-5sin²(x/2)-4sin²(x/2)-4cos²(x/2)=0
9sin²(x/2)-8sin(x/2)cos(x/2)-cos²(x/2)=0/cos²(x/2)=0
9tg²(x/2)-8tg(x/2)-1=0
tg(x/2)=a
9a²-8a-1)=0
D=64+36=100
a1=(8-10)/18=-1/9⇒tg(x/2)=-1/9⇒x/2=-arctg1/9+πn⇒x=-2arctg2/9+2πn
a2=(8+10)/18=1⇒tg(x/2)=1⇒x/2=π/4+πn⇒x=π/2+2πn
2)(1-cos2x)²/4+(1+cos2x)²/4=cos²2x+0,25
1-2cos2x+cos²2x+1+2cos2x+cos²2x=4cos²2x+1
4cos²2x-2cos²2x-2+1=0
2cos²2x-1=0
cos4x=0
4x=π/2+πn
x=π/8+πn/4