sin^2 x/2-cos^2 x/2=cos2x

[tex]sin^2 \frac{x}{2}-cos^2 \frac{x}{2}=cos (2x)[/tex]
[tex]-(cos^2 \frac{x}{2}-sin^2 \frac{x}{2})=cos (2x)[/tex]
[tex]-cos (2*\frac{x}{2})=2cos^2 x-1[/tex]
[tex]-cos x=2cos^2 x-1[/tex]
[tex]2cos^2 x+cos x-1=0[/tex]
[tex](2cos x-1)(cos x+1)=0[/tex]
[tex]2cos x-1=0;cos x=\frac{1}{2};x=^+_-\frac{\pi}{3}+2*\pi*n[/tex]
n є Z
[tex]cos x+1=0;cos x=-1;x=\pi+2*\pi*k[/tex]
k є Z