A) \[\sec \theta -\tan \theta \]
B) \[\sec \theta +\tan \theta \]
C) \[\text{cosec}\theta \text{+cot}\theta \]
D) \[\text{cosec}\theta -\cot \theta \]
Correct Answer: B
Solution :
\[\sqrt{\frac{1+\sin \theta }{1-\sin \theta }}=\sqrt{\frac{(1+\sin \theta )(1+\sin \theta )}{(1-\sin \theta )(1+\sin \theta )}}\] \[=\sqrt{\frac{{{(1+\sin \theta )}^{2}}}{1-{{\sin }^{2}}\theta }}=\sqrt{\frac{{{(1+\sin \theta )}^{2}}}{{{\cos }^{2}}\theta }}=\frac{1+\sin \theta }{\cos \theta }\] \[=\frac{1}{\cos \theta }+\frac{\sin \theta }{\cos \theta }=\sec \theta +\tan \theta \]
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