The power-reducing formula,

sin^{2}u = (1 - cos 2u)/2,

can be used in cases other than u = x.

Here you need to replace u, in each instance, with x/2.

This results in the relevant formula to your case,

sin^{2}x/2 = (1 - cos 2(x/2))/2 or

sin^{2}x/2 = (1 - cos x)/2.

Hope this helps.