A) \[\left\{ \frac{\pi }{3} \right\}\]
B) \[\left\{ \frac{\pi }{3},\frac{5\pi }{3} \right\}\]
C) \[\left\{ \frac{\pi }{3},\frac{5\pi }{3},{{\cos }^{-1}}\left( -\frac{3}{2} \right) \right\}\]
D) None of the above
Correct Answer: B
Solution :
Given, \[(2\text{ }cos\text{ }x-1)(3+2\text{ }cos\text{ }x)=0\] \[\Rightarrow \] \[\cos x=\frac{1}{2},\cos x\ne -\frac{3}{2}\] \[\Rightarrow \] \[x=\frac{\pi }{3},\frac{5\pi }{3}\in (0,2\pi )\]
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