A) \[\frac{1}{2}\tan \theta \]
B) \[\frac{1}{2}\cot \theta \]
C) \[\tan \theta \]
D) \[\cot \theta \]
Correct Answer: C
Solution :
\[\frac{\sin \theta +\sin 2\theta }{1+\cos \theta +\cos 2\theta }\] \[=\frac{\sin \theta +2\sin \theta \cos \theta }{2{{\cos }^{2}}\theta +\cos \theta }=\frac{\sin \theta (1+2\cos \theta )}{\cos \theta (1+2\cos \theta )}=\tan \theta \]. Trick: Put\[\theta =30{}^\circ \], since for \[\theta =30{}^\circ \]no option will give the common value.
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