Prove. A A 1- A =1+ A - Vidyadip

Question

Prove.
$\frac{\sin A \tan A}{1-\cos A}=1+\sec A$

✓

Answer

$\text { LHS }=\frac{\sin A \tan A}{1-\cos A} $
$ =\frac{\sin A \tan A}{1-\cos A} \times \frac{1+\cos A}{1+\cos A} $
$ =\frac{\sin A \tan A(1+\cos A)}{1-\cos ^2 A} $
$=\frac{\sin A \frac{\sin A}{\cos A}(1+\cos A)}{\sin ^2 A} $
$ =\frac{1+\cos A}{\cos A}$
$ =\frac{1}{\cos A}+\frac{\cos A}{\cos A} $
$ =\sec A+1$

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