A) \[2n\pi \pm \frac{\pi }{3}\]
B) \[n\pi ,2n\pi \pm \frac{2\pi }{3}\]
C) \[n\pi ,2n\pi \pm \frac{\pi }{3}\]
D) \[n\pi ,\,\,n\pi +\frac{2\pi }{3}\]
Correct Answer: B
Solution :
\[2\sin \theta +\tan \theta =0\]; \[\sin \theta \left( 2+\frac{1}{\cos \theta } \right)=0\] i.e., \[\sin \theta =0\Rightarrow \theta =n\pi \] or \[\frac{1}{\cos \theta }=-2\Rightarrow \cos \theta =-\frac{1}{2}\Rightarrow \theta =2n\pi \pm \left( \frac{2\pi }{3} \right)\].
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