Prove that:
$$\sqrt{\frac{\sec A - 1}{\sec A + 1}} + \sqrt{\frac{\sec A + 1}{\sec A - 1}} = 2 \cosec A$$

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Step 1: LHS $= \frac{\sqrt{\sec A - 1}}{\sqrt{\sec A + 1}} + \frac{\sqrt{\sec A + 1}}{\sqrt{\sec A - 1}} = \frac{\sec A - 1 + \sec A + 1}{\sqrt{\sec^2 A - 1}}$
Step 2: $= \frac{2 \sec A}{	an A}$
Step 3: $= \frac{2}{\cos A} 	imes \frac{\cos A}{\sin A} = \frac{2}{\sin A} = 2 \cosec A$ = RHS

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