Use the trigonometric identity $\operatorname{cos}(2θ) = 2\operatorname{cos}^2 θ − 1$ to rewrite the expressions below.

1. $\operatorname{sin}^2 x$

   Step (a):

   $2\cos^2(x)=\cos(2x)+1$

2. $\operatorname{cos}^2 x$

   Hint (b):

   $\cos^2(x)=1-\sin^2(x)$

   Step (b):

   $\cos(2x)=2(1-\sin^2(x))-1$
   Now solve for $\operatorname{sin}^2(x)$.