A) \[2\pi \]
B) \[\pi \]
C) \[\frac{2\pi }{3}\]
D) \[\frac{\pi }{3}\]
Correct Answer: C
Solution :
\[\frac{\sin \theta +\sin 2\theta }{\cos \theta +\cos 2\theta }=\frac{2\sin \left( \frac{3\theta }{2} \right)\cos \left( \frac{\theta }{2} \right)}{2\cos \left( \frac{3\theta }{2} \right)\cos \left( \frac{\theta }{2} \right)}=\tan \left( \frac{3\theta }{2} \right)\]Hence proved\[=\frac{2\pi }{3}\]
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