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