A) \[2n\pi \pm \frac{\pi }{3}\]
B) \[n\pi +\frac{\pi }{3}\]
C) \[n\pi \pm \frac{\pi }{3}\]
D) None of these [Where \[n\] is an integer]
Correct Answer: C
Solution :
\[\frac{3+2i\sin \theta }{1-2i\sin \theta }\] will be purely imaginary, if the real part vanishes, i.e., \[\frac{3-4{{\sin }^{2}}\theta }{1+4{{\sin }^{2}}\theta }=0\] Þ \[3-4{{\sin }^{2}}\theta =0\] (only if \[\theta \] be real) Þ \[\sin \theta =\pm \frac{\sqrt{3}}{2}=\sin \left( \pm \frac{\pi }{3} \right)\] Þ \[\theta =n\pi +{{(-1)}^{n}}\left( \pm \frac{\pi }{3} \right)=n\pi \pm \frac{\pi }{3}\]
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