A) \[\frac{\pi }{12}\]
B) \[\frac{\pi }{6}\]
C) \[\frac{\pi }{4}\]
D) \[\frac{\pi }{2}\]
Correct Answer: B
Solution :
Given expression \[\sin 5\theta -\sin 3\theta +\sin \theta =0;\theta \in (0,\pi /2)\] \[(\sin 5\theta +\sin \theta )=\sin 3\theta \] \[2.\sin 3\theta .\cos 2\theta =\sin 3\theta \] \[\Rightarrow \] \[\sin 3\theta (2\cos 2\theta -1)=0\] \[\sin 3\theta =0\] and \[2\cos 2\theta =1\] \[\Rightarrow \]\[\sin 3\theta =\sin {{0}^{o}}\]and\[\cos 2\theta =1/2=\cos \pi /3\] \[\Rightarrow \] \[3\theta =0,\pi \] and \[2\theta =\pi /3\] \[\Rightarrow \] \[\theta =0,\pi /3\] and \[\theta =\pi /6\] So, the value of 9 satisfying given expression is \[\theta =\pi /3,\,\,\pi /6\].
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