A) \[\frac{\pi }{4},\frac{5\pi }{12},\frac{\pi }{2},\frac{2\pi }{3},\frac{3\pi }{4},\frac{8\pi }{9}\]
B) \[\frac{2\pi }{9},\frac{\pi }{4},\frac{\pi }{2},\frac{2\pi }{3},\frac{3\pi }{4},\frac{35\pi }{36}\]
C) \[\frac{2\pi }{9},\frac{\pi }{4},\frac{\pi }{2},\frac{2\pi }{3},\frac{3\pi }{4},\frac{8\pi }{9}\]
D) \[\frac{2\pi }{9},\frac{\pi }{4},\frac{4\pi }{9},\frac{\pi }{2},\frac{3\pi }{4},\frac{8\pi }{9}\]
Correct Answer: D
Solution :
\[\sin 4\theta +2\sin 4\theta \cos 3\theta =0\]\[\because \]\[\theta ,\in (0,\pi )\] \[\sin 4\theta (1+2cos3\theta )=0\] \[\sin 4\theta =0\] or \[\cos 3\theta =-\frac{1}{2}\] \[4\theta =n\pi ;n\in I\] or \[3\theta =2n\pi \pm \frac{2\pi }{3},n\in I\] \[\theta =\frac{\pi }{4},\frac{\pi }{2},\frac{3\pi }{4}\] or \[\theta =\frac{2\pi }{9},\frac{8\pi }{9},\frac{4\pi }{9}\]
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