A) \[n\pi +\frac{\pi }{5}\]
B) \[\left( n+\frac{1}{6} \right)\frac{\pi }{5}\]
C) \[\left( 2n\pm \frac{1}{6} \right)\frac{\pi }{5}\]
D) \[\left( n+\frac{1}{3} \right)\frac{\pi }{5}\]
Correct Answer: B
Solution :
\[\sqrt{3}\tan 2\theta +\sqrt{3}\tan 3\theta +\tan 2\theta \tan 3\theta =1\] \[\Rightarrow \] \[\frac{\tan 2\theta +\tan 3\theta }{1-\tan 2\theta \tan 3\theta }=\frac{1}{\sqrt{3}}\] Þ \[\tan 5\theta =\tan \frac{\pi }{6}\] \[\Rightarrow \] \[5\theta =n\pi +\frac{\pi }{6}\Rightarrow \theta =\left( n+\frac{1}{6} \right)\frac{\pi }{5}\].
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