A) \[\frac{n\pi }{4}\]or \[n\pi \pm \frac{\pi }{3}\]
B) \[\frac{n\pi }{4}\]or \[n\pi \pm \frac{\pi }{6}\]
C) \[\frac{n\pi }{4}\]or \[2n\pi \pm \frac{\pi }{6}\]
D) None of these
Correct Answer: A
Solution :
\[\sin 6\theta +\sin 4\theta +\sin 2\theta =0\] \[\Rightarrow 2\sin 4\theta \cos 2\theta +\sin 4\theta =0\] \[\Rightarrow \]\[\sin 4\theta (2\cos 2\theta +1)=0\] \[\Rightarrow \] \[2\cos 2\theta =-1\] \[\Rightarrow \] \[\cos 2\theta =-\frac{1}{2}\] \[\Rightarrow \] \[2\theta =2n\pi \pm \frac{2\pi }{3}\Rightarrow \theta =n\pi \pm \frac{\pi }{3}\] and \[\sin 4\theta =0\Rightarrow 4\theta =n\pi \Rightarrow \theta =\frac{n\pi }{4}\] \[\theta =\frac{n\pi }{4}\] or \[n\pi \pm \frac{\pi }{3}\].
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