A) \[\left( n+\frac{1}{2} \right)\frac{\pi }{3}\]
B) \[\left( n\frac{1}{2} \right)\pi \]
C) \[\left( 2n\pm \frac{1}{2} \right)\frac{\pi }{3}\]
D) None of these
Correct Answer: A
Solution :
\[\tan 2\theta \tan \theta =1\] \[\Rightarrow \] \[\text{tan}2\theta =\cot \theta \] \[\Rightarrow \] \[2\theta =\tan \left( \pi /2-\theta \right)\] \[\Rightarrow \] \[2\theta =n\pi +\left( \pi /2-\theta \right)\] \[\Rightarrow \] \[3\theta =n\pi +\pi /2\] \[\therefore \] \[\theta =\left( n+\frac{1}{2} \right)\frac{\pi }{3}\]
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