Answer
$$\csc^2\theta+\sec^2\theta=\frac{1}{\sin^2\theta\cos^2\theta}$$
Work Step by Step
$$A=\csc^2\theta+\sec^2\theta$$
$\csc\theta$ and $\sec\theta$ can be written according to the following identities:
$$\csc\theta=\frac{1}{\sin\theta}\hspace{2cm}\sec\theta=\frac{1}{\cos\theta}$$
So,
$$A=\frac{1}{\sin^2\theta}+\frac{1}{\cos^2\theta}$$
$$A=\frac{\cos^2\theta+\sin^2\theta}{\sin^2\theta\cos^2\theta}$$
- Recall the identity $\cos^2\theta+\sin^2\theta=1$
$$A=\frac{1}{\sin^2\theta\cos^2\theta}$$
This is the answer we need to the question.
