A) \[2n\pi \pm \frac{\pi }{6}\]
B) \[2n\pi \pm \frac{\pi }{3}\]
C) \[n\pi \pm \frac{\pi }{3}\]
D) \[n\pi \pm \frac{\pi }{6}\]
Correct Answer: D
Solution :
\[\cot \theta +\cot \left( \frac{\pi }{4}+\theta \right)=2\Rightarrow \frac{\cos \theta }{\sin \theta }+\frac{\cos \{(\pi /4)+\theta \}}{\sin \{(\pi /4)+\theta \}}=2\] \[\Rightarrow \] \[\sin \left( \frac{\pi }{4}+2\theta \right)=2\sin \theta \sin \left( \frac{\pi }{4}+\theta \right)\] \[\Rightarrow \] \[\sin \left( \frac{\pi }{4}+2\theta \right)+\cos \left( \frac{\pi }{4}+2\theta \right)=\frac{1}{\sqrt{2}}\] \[\Rightarrow \] \[\cos 2\theta =\frac{1}{2}\Rightarrow 2\theta =2n\pi \pm \frac{\pi }{3}\Rightarrow \theta =n\pi \pm \frac{\pi }{6}\].
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