sin'(x/2)=cos(x/2)(x/2)'=cos(x/2)/2
[(sinx)^2]'=2sinx(sinx)'=2sinxcosx=sin(2x)
[sin(x/2)]^2 '=2sin(x/2)[sin(x/2)]'=2sin(x/2)cos(x/2)(x/2)'=sinx/2