Answer
$$\frac{\cot\theta}{\sec\theta}=\frac{\cos^2\theta}{\sin\theta}$$
Work Step by Step
$$A=\frac{\cot\theta}{\sec\theta}$$
We need to rewrite $\cot\theta$ and $\sec\theta$ in terms of $\sin\theta$ and $\cos\theta$, using the following identities
$$\cot\theta=\frac{\cos\theta}{\sin\theta}\hspace{2cm}\sec\theta=\frac{1}{\cos\theta}$$
$$A=\frac{\frac{\cos\theta}{\sin\theta}}{\frac{1}{\cos\theta}}$$
$$A=\frac{\cos\theta\times\cos\theta}{\sin\theta\times1}$$
$$A=\frac{\cos^2\theta}{\sin\theta}$$
It could not be simplified to any simpler form, so we stop here.
