Answer
$$\cos\theta(\cos\theta-\sec\theta)=-\sin^2\theta$$
Work Step by Step
$$A=\cos\theta(\cos\theta-\sec\theta)$$
- Reciprocal Identity:
$$\sec\theta=\frac{1}{\cos\theta}$$
Replace into $A$:
$$A=\cos\theta(\cos\theta-\frac{1}{\cos\theta})$$
$$A=\cos^2\theta-\cos\theta\times\frac{1}{\cos\theta}$$
$$A=\cos^2\theta-1$$
$$A=-(1-\cos^2\theta)$$
- Pythagorean Identity:
$$\sin^2\theta=1-\cos^2\theta$$
Replace into $A$:
$$A=-\sin^2\theta$$