Prove that $\frac{1 + \sec A}{\sec A} = \frac{\sin^2 A}{1 - \cos A}$.

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Step 1: LHS $= \frac{1 + \sec A}{\sec A} = \frac{1 + \frac{1}{\cos A}}{\frac{1}{\cos A}} = 1 + \cos A$.
Step 2: $= \frac{(1 - \cos A)(1 + \cos A)}{(1 - \cos A)} = \frac{1 - \cos^2 A}{1 - \cos A}$.
Step 3: $= \frac{\sin^2 A}{1 - \cos A} = $ RHS. Hence proved.

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