Question
Prove the following identitie:
$\sqrt{\frac{1+\sin A}{1-\sin A}}=\frac{\cos A}{1-\sin A}$
$\sqrt{\frac{1+\sin A}{1-\sin A}}=\frac{\cos A}{1-\sin A}$
✓
Answer
$\sqrt{\frac{1+\sin A}{1-\sin A}}$
$=\sqrt{\frac{1+\sin A}{1-\sin A} \times \frac{1-\sin A}{1-\sin A}} $
$=\sqrt{\frac{1-\sin ^2 A}{(1-\sin A)^2}}$
$ =\sqrt{\frac{\cos ^2 A}{(1+\sin A)^2}} $
$=\frac{\cos A}{1-\sin A}$
$=\sqrt{\frac{1+\sin A}{1-\sin A} \times \frac{1-\sin A}{1-\sin A}} $
$=\sqrt{\frac{1-\sin ^2 A}{(1-\sin A)^2}}$
$ =\sqrt{\frac{\cos ^2 A}{(1+\sin A)^2}} $
$=\frac{\cos A}{1-\sin A}$
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