The power-reducing formula,
sin2 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,
sin2 x/2 = (1 - cos 2(x/2))/2 or
sin2 x/2 = (1 - cos x)/2.
Hope this helps.