A) \[\frac{n\pi }{6},\frac{n\pi }{3}+{{(-1)}^{n}}\frac{\pi }{18}\]
B) \[\frac{n\pi }{3},\frac{n\pi }{3}+{{(-1)}^{n}}\frac{\pi }{18}\]
C) \[\frac{n\pi }{4},\frac{n\pi }{3}\pm \frac{\pi }{18}\]
D) \[\frac{n\pi }{4},\frac{n\pi }{3}+{{(-1)}^{n}}\frac{\pi }{18}\]
Correct Answer: D
Solution :
\[\cos 7\theta =\cos \theta -\sin 4\theta \Rightarrow \sin 4\theta =\cos \theta -\cos 7\theta \] \[\Rightarrow \,\,\,\sin 4\theta =2\sin 4\theta \sin 3\theta \] \[\Rightarrow \,\,\sin 4\theta (1-2\sin 3\theta )=0\] \[\therefore \,\,\,\sin 4\theta =0\] or \[\sin 3\theta =\frac{1}{2}\] \[\Rightarrow \,\,\,4\theta =n\pi \] or \[3\theta =n\pi +{{(-1)}^{n}}\frac{\pi }{6}\] \[\Rightarrow \,\,\,\theta =\frac{n\pi }{4}\] or \[\frac{n\pi }{3}+{{(-1)}^{n}}\frac{\pi }{18}\]
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