A) \[\theta =\frac{n\pi }{7}+\frac{\pi }{14}\]
B) \[\theta =\frac{n\pi }{7}+\frac{\pi }{5}\]
C) \[\theta =\frac{n\pi }{7}+\frac{\pi }{2}\]
D) \[\theta =\frac{n\pi }{7}+\frac{\pi }{3},n\in Z\]
Correct Answer: A
Solution :
\[\tan 5\theta =\cot 2\theta \Rightarrow \tan 5\theta =\tan \left( \frac{\pi }{2}-2\theta \right)\] therefore \[5\theta =n\pi +\frac{\pi }{2}-2\theta \] \[7\theta =n\pi +\frac{\pi }{2}\] \[\theta =\frac{n\pi }{7}+\frac{\pi }{14}\]
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