Question : The value of $\sqrt{\frac{1+\sin A}{1-\sin A}}$ is:
Option 1: $\sec A-\tan A$
Option 2: $\operatorname{cosec} A+\cot A$
Option 3: $\sec A+\tan A$
Option 4: $\operatorname{cosec} A-\cot A$
Correct Answer: $\sec A+\tan A$
Solution :
$\sqrt{\frac{1+\sin A}{1-\sin A}}$
= $\sqrt{\frac{(1+\sin A)^2}{(1-\sin A)(1+\sin A)}}$
= $\sqrt{\frac{(1+\sin A)^2}{1-\sin^2 A}}$
= $\sqrt{\frac{(1+\sin A)^2}{\cos^2 A}}$
= $\frac{(1+\sin A)}{\cos A}$
= $\sec A + \tan A$
Hence, the correct answer is $\sec A + \tan A$.
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