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