Answer
$${\text{si}}{{\text{n}}^2}x = \frac{{1 - \cos 2x}}{2}{\text{ and co}}{{\text{s}}^2}x = \frac{{1 + \cos 2x}}{2}$$
Work Step by Step
$$\eqalign{
& {\text{The half - angle identities to integrate si}}{{\text{n}}^2}x{\text{ and co}}{{\text{s}}^2}x{\text{ are:}} \cr
& {\text{si}}{{\text{n}}^2}x = \frac{{1 - \cos 2x}}{2}{\text{ and co}}{{\text{s}}^2}x = \frac{{1 + \cos 2x}}{2} \cr} $$
