A) 1
B) 2
C) 3
D) 4
E) 0
Correct Answer: C
Solution :
We have\[\cos 2\theta =\sin \theta \] \[\Rightarrow \] \[\cos 2\theta =\cos \left( \frac{\pi }{2}-\theta \right)\] \[\Rightarrow \] \[2\theta =2n\pi \pm \left( \frac{\pi }{2}-\theta \right),n\in Z\] Taking + sign, we have \[\theta =\frac{2n\pi }{3}+\frac{\pi }{6},n\in Z\] \[\Rightarrow \] \[\theta =\frac{\pi }{6}+\frac{5\pi }{6}\in (0,2\pi )\] Taking - sign, we have \[\theta =2n\pi -\frac{\pi }{2},n\in Z\] \[\theta =\frac{3\pi }{2}\] \[\Rightarrow \] \[\theta =\frac{3\pi }{2}\in (0,2\pi )\] Hence, there are three solutions.
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