A) \[\theta =(6n+1)\pi /18,\,\forall n\in I\]
B) \[\theta =(6n+1)\pi /9,\,\forall n\in I\]
C) \[\theta =(3n+1)\pi /9,\,\forall n\in I\]
D) None of these
Correct Answer: B
Solution :
Given relation is \[\tan \theta +\tan 2\theta +\sqrt{3}\tan \theta \tan 2\theta =\sqrt{3}\] Þ \[\,\tan \theta +\tan 2\theta =\sqrt{3}(1-\tan \theta \tan 2\theta )\] Þ \[\frac{\tan \theta +\tan 2\theta }{1-\tan \theta \tan 2\theta }\]= \[\sqrt{3}\] Þ \[\tan 3\theta =\tan (\pi /3)\] Þ \[3\theta =n\pi +\frac{\pi }{3}\] Þ \[\theta =(3n+1)\frac{\pi }{9}\].
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