A) \[\frac{\pi }{6},\frac{7\pi }{6}\]
B) \[\frac{\pi }{3},\frac{5\pi }{3}\]
C) \[\frac{\pi }{3},\frac{7\pi }{3}\]
D) None of these
Correct Answer: B
Solution :
\[2-2{{\cos }^{2}}\theta =3\cos \theta \] Þ \[2{{\cos }^{2}}+3\cos \theta -2=0\] Þ \[\cos \theta =\frac{-3\pm \sqrt{9+16}}{4}=\frac{-3\pm 5}{4}\] Neglecting (-) sign, we get \[\cos \theta =\frac{1}{2}=\cos \left( \frac{\pi }{3} \right)\] \[\Rightarrow \] \[\theta =2n\pi \pm \frac{\pi }{3}\]. The values of \[\theta \] between 0 and \[2\pi \] are \[\frac{\pi }{3},\text{ }\frac{\text{5}\pi }{\text{3}}\].
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