derive the half angle formula for sine, sin (X/2) = squaroot((1-cosx)/2) from a double angle formula for cosine.

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

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

sin^{2}(u)=\frac{1-cos(2u)}{2}

Now, use the substitution u=\frac{x}{2}