A) \[\frac{\pi }{9},\frac{\pi }{4}\]
B) \[\frac{\pi }{3},\frac{\pi }{9}\]
C) \[\frac{\pi }{6},\frac{\pi }{9}\]
D) \[\frac{\pi }{3},\frac{\pi }{4}\]
Correct Answer: A
Solution :
\[\sin 7\theta +\sin \theta -\sin 4\theta =0\] \[\Rightarrow \] \[2\sin 4\theta \cos 3\theta -\sin 4\theta =0\] \[\Rightarrow \] \[\sin 4\theta (2\cos 3\theta -1)=0\Rightarrow \sin 4\theta =0,\,\text{ }\cos 3\theta =\frac{1}{2}\] Now sin\[4\theta =0\] \[\Rightarrow \] \[4\theta =\pi \] \[\Rightarrow \] \[\theta =\frac{\pi }{4}\]. and \[\cos 3\theta =\frac{1}{2}\] \[\Rightarrow \] \[3\theta =\frac{\pi }{3}\] \[\Rightarrow \] \[\theta =\frac{\pi }{9}\].
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