Answer
$$\sin^{2}\theta$$
Work Step by Step
Simplify
$$\sec\theta\cos\theta-\cos^{2}\theta.$$
Use the Reciprocal Identity
$$\sec\theta=\frac{1}{\cos\theta}$$
to obtain
$$\sec\theta\cos\theta-\cos^{2}\theta=\bigg(\frac{1}{\cos\theta}\bigg)\cos\theta-\cos^{2}\theta=1-\cos^{2}\theta.$$
The Pythagorean Identity states
$$\sin^{2}\theta+\cos^{2}\theta=1$$
or
$$1-\cos^{2}\theta=\sin^{2}\theta.$$
So
$$\sec\theta\cos\theta-\cos^{2}\theta=\sin^{2}\theta.$$
