A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{3},\frac{5\pi }{3}\]
C) \[\frac{\pi }{2},\frac{5\pi }{3},{{\cos }^{-1}}\left( -\frac{3}{2} \right)\]
D) \[\frac{5\pi }{3}\]
Correct Answer: B
Solution :
\[(2\cos x-1)\,\,(3+2\cos x)=0\] Then \[\cos x=\frac{1}{2}\text{ as}\,\text{ }\cos x\ne \frac{-3}{2}\] \[\Rightarrow \] \[x=2n\pi \pm \frac{\pi }{3};\,\,\left\{ \begin{align} & \text{ for }n=0,\,\,x=\frac{\pi }{3},\,\frac{5\pi }{3} \\ & \text{ for }n=1,\,\,x=\frac{5\pi }{3} \\ \end{align} \right\}\]
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