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Prove that : $\sqrt{\frac{\sec \text{ A}-1}{\sec \text{ A}+1}} + \sqrt{\frac{\sec \text{ A}+1}{\sec \text{ A}-1}} = 2 \text{ cosec A}$
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LHS $$\begin{aligned}& = \frac{\sec \text{A}-1 + \sec \text{A}+1}{\sqrt{\sec^2 \text{A}-1}} \\ & = \frac{2\sec \text{A}}{\tan \text{A}} \\ & = 2\text{cosec A} = \text{RHS}\end{aligned}$$