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