Question
Prove.$\sqrt{\frac{1-\sin A}{1+\sin A}}=\frac{\cos A}{1+\sin A}$
✓
Answer
$\text { LHS }=\sqrt{\frac{1-\sin A}{1+\sin A}}$
$=\sqrt{\frac{1-\sin A}{1+\sin A} \times \frac{1+\sin A}{1+\sin A}}$
$=\sqrt{\frac{1-\sin ^2 A}{(1+\sin A)^2}}$
$=\sqrt{\frac{\cos ^2 A}{(1+\sin A)^2}}$
$\frac{\cos A}{1+\sin A}=\text { RHS }$
$=\sqrt{\frac{1-\sin A}{1+\sin A} \times \frac{1+\sin A}{1+\sin A}}$
$=\sqrt{\frac{1-\sin ^2 A}{(1+\sin A)^2}}$
$=\sqrt{\frac{\cos ^2 A}{(1+\sin A)^2}}$
$\frac{\cos A}{1+\sin A}=\text { RHS }$
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