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