A) \[(2n+1)\frac{\pi }{4}\]
B) \[(2n+1)\frac{\pi }{6}\]
C) \[(2n+1)\frac{\pi }{2}\]
D) \[\frac{1}{1}(2n+1)\frac{\pi }{3}\]
Correct Answer: B
Solution :
We have \[\tan 2\theta \,.\,\,\tan \theta =1\] \[\Rightarrow \] \[\tan 2\theta =\frac{1}{\tan \theta }\] \[\Rightarrow \] \[\tan 2\theta =\cot \theta \] \[\Rightarrow \] \[\tan 2\theta =\tan \left( \frac{\pi }{2}-\theta \right)\] \[\left[ \cot \theta =\tan \left( \frac{\pi }{2}-\theta \right) \right]\] \[\Rightarrow \] \[2\theta =\frac{\pi }{2}-\theta \] \[\Rightarrow \] \[3\theta =n\pi +\frac{\pi }{2}\] \[\Rightarrow \] \[3\theta =(2n+1)\pi /2\] \[\Rightarrow \] \[\theta =\frac{\pi }{6}\,(2n+1)\]
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