A) 2
B) \[\frac{2}{\sin \theta }\]
C) \[\frac{4}{\sin \theta \cos \theta }\]
D) None of these
Correct Answer: B
Solution :
Given expression \[\frac{{{\sin }^{2}}\theta +{{(1+\cos \theta )}^{2}}}{(1+\cos \theta )\sin \theta }\] \[=\frac{{{\sin }^{2}}\theta +\cos {{\theta }^{2}}+1+2\cos \theta }{(1+\cos \theta )\sin \theta }\] \[=\frac{(2+2\cos \theta )}{(1+\cos \theta )\sin \theta }\] \[=\frac{2(1+\cos \theta )}{(1+\cos \theta )\sin \theta }=\frac{2}{\sin \theta }\]
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