A) \[\theta =2m\pi \pm \pi /4\]
B) \[\theta =m\pi +{{(-1)}^{n}}2\pi /3\]
C) \[\theta =m\pi +{{(-1)}^{n}}\pi /3\]
D) \[\theta =2m\pi \pm 2\pi /3\]
Correct Answer: D
Solution :
Given that,\[\cos \theta +\cos 2\theta +\cos 3\theta =0\] \[\Rightarrow \] \[(\cos \theta +\cos 3\theta )+\cos 2\theta =0\] \[\Rightarrow \] \[2\cos 2\theta \cos \theta +\cos 2\theta =0\] \[\Rightarrow \] \[\cos 2\theta (2\cos \theta +1)=0\] \[\Rightarrow \] \[\cos 2\theta =0\]and\[2\cos \theta +1=0\] \[\Rightarrow \] \[2\theta =\cos \frac{\pi }{2}\] and \[\cos \theta =-\frac{1}{2}\] \[\Rightarrow \] \[\theta =m\pi \pm \frac{\pi }{4}\]and\[\theta =2m\pi \pm \frac{2\pi }{3}\]
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