sin^2x-cos^2x=cos(x/2)

sin²x-cos²x=cosx/2
-cos2x=cosx/2
cosx/2+cos2x=0
2cos5x/4*cos3x/4=0
cos5x/4=0⇒5x/4=π/2+πn⇒x=2π/5+4πn/5,n∈z
cos3x/4=0⇒3x/4=π/2+πn⇒x=2π/3+4πn/3,n∈z