A) \[\frac{5\pi }{6}\]
B) \[\frac{2\pi }{3}\]
C) \[\frac{\pi }{3}\]
D) \[\frac{\pi }{6}\]
Correct Answer: A
Solution :
\[2-2{{\cos }^{2}}\theta +\sqrt{3}\cos \theta +1=0\] \[\Rightarrow \] \[2{{\cos }^{2}}\theta -\sqrt{3}\cos \theta -3=0\] \[\Rightarrow \] \[\cos \theta =\frac{\sqrt{3}\pm \sqrt{3+24}}{4}=\frac{\sqrt{3}(1\pm 3)}{4}=\sqrt{3}\left( -\frac{1}{2} \right)\] \[\Rightarrow \] \[\theta =\frac{5\pi }{6}\].
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