Answer
$$\frac{1}{\csc^2\theta}+\frac{1}{\sec^2\theta}=1$$
Work Step by Step
$$A=\frac{1}{\csc^2\theta}+\frac{1}{\sec^2\theta}$$
$$A=\Bigg(\frac{1}{\csc\theta}\Bigg)^2+\Bigg(\frac{1}{\sec\theta}\Bigg)^2$$
- Reciprocal Identities:
$$\csc\theta=\frac{1}{\sin\theta}\hspace{2cm}\sec\theta=\frac{1}{\cos\theta}$$
Therefore, $$\frac{1}{\csc\theta}=\sin\theta\hspace{2cm}\frac{1}{\sec\theta}=\cos\theta$$
$$A=\sin^2\theta+\cos^2\theta$$
$$A=1$$ (Pythagorean Identity)
