A) \[\theta =2m\pi \pm \frac{2\pi }{3}\]
B) \[\theta =2m\pi \pm \frac{\pi }{4}\]
C) \[\theta =m\pi \pm {{(-1)}^{m}}\frac{2\pi }{3}\]
D) \[x=m\pi +{{(-1)}^{m}}\frac{\pi }{3}\]
Correct Answer: A
Solution :
\[\cos \theta +\cos 2\theta +\cos 3\theta =0\] Þ \[(\cos \theta +\cos 3\theta )+\cos 2\theta =0\] Þ \[2\cos 2\theta \cos \theta +\cos 2\theta =0\] Þ \[\cos 2\theta (2\cos \theta +1)=0\] Þ \[\cos 2\theta =0=\cos \frac{\pi }{2}\] Þ \[\theta =\frac{\pi }{4}\]Þ \[\theta =2m\pi \pm \frac{\pi }{4}\] or \[\cos \theta =\frac{-1}{2}=\cos \frac{2\pi }{3}\] Þ \[\theta =2m\pi \pm \frac{2\pi }{3}\].
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