A) \[\sec \theta \]
B) \[2\sec \theta \]
C) \[\frac{1}{2}\cos \theta \]
D) \[2\cos \theta \]
Correct Answer: B
Solution :
\[?=\frac{1+\sin \,\,\theta }{\cos \,\,\theta }+\frac{\cos \,\,\theta }{1+\sin \,\,\theta }\] \[=\frac{1+{{\sin }^{2}}\,\,\theta +2\,\,\sin \,\,\theta +{{\cos }^{2}}\,\,\theta }{\cos \,\,\theta \,\,(1+\sin \,\,\theta )}\] \[=\frac{2+2\,\,\sin \,\,\theta }{\cos \,\,\theta \,\,(1+sin\,\,\theta )}\] \[=\frac{2\,\,(1+sin\,\,\theta )}{\cos \,\,\theta (1+sin\,\,\theta )}\] \[=\frac{2}{\cos \,\,\theta }=2\,\,\sec \,\,\theta \]
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