Prove that: $\sqrt{\frac{1 + \sin A}{1 - \sin A}} = \sec A + an A$

Question

Prove that: $\sqrt{\frac{1 + \sin A}{1 - \sin A}} = \sec A + 	an A$

Accepted Answer

Step 1: LHS $= \sqrt{\frac{1 + \sin A}{1 - \sin A}} = \sqrt{\frac{(1 + \sin A)(1 + \sin A)}{(1 - \sin A)(1 + \sin A)}}$
Step 2: $= \sqrt{\frac{(1 + \sin A)^2}{1 - \sin^2 A}} = \sqrt{\frac{(1 + \sin A)^2}{\cos^2 A}}$
Step 3: $= \frac{1 + \sin A}{\cos A} = \frac{1}{\cos A} + \frac{\sin A}{\cos A}$
Step 4: $= \sec A + 	an A =$ RHS

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