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