Question

$ \sqrt{\frac{1+\sin \theta}{1-\sin \theta}}= $

• A. $\sec \theta+\tan \theta$
• B. $\sec \theta-\cot \theta$
• C. $\operatorname{cosec} \theta+\tan \theta$
• D. $\operatorname{cosec} \theta-\tan \theta$

Answer 1

Answer: (A)

$\sqrt{\frac{1+\sin \theta}{1-\sin \theta}}=\sqrt{\frac{(1+\sin \theta)(1+\sin \theta)}{(1-\sin \theta)(1+\sin \theta)}}$
$=\sqrt{\frac{(1+\sin \theta)^2}{1-\sin ^2 \theta}} $
$=\frac{1+\sin \theta}{\cos \theta}=\sec \theta+\tan \theta$