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 :
\[\tan 2\theta =\cot \theta \] Þ \[\tan 2\theta =\tan \text{ }\left( \frac{\pi }{2}-\theta \right)\] \[\Rightarrow \] \[2\theta =n\pi +\frac{\pi }{2}-\theta \Rightarrow \theta =\frac{n\pi }{3}+\frac{\pi }{6}\].
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