Answer
$$\cos^2 x\sin^2 x = \frac{1-\cos 4 x}{8}$$
Work Step by Step
We use the know identities to obtain:
\begin{align*}
\cos^2 x\sin^2 x&= \left(\cos x\sin x\right)^2\\
&= \left( \frac{\sin2 x}{2}\right)^2\\
&=\frac{\sin^22x}{4},\\
& \text{Use: } \sin^2 x=\frac{1}{2}[1-\cos 2x] \\
&= \frac{1-\cos 4 x}{8} \\
\end{align*}
