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

Question

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

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Answer

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

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