A) \[n\pi \pm \frac{\pi }{3}\]
B) \[2n\pi \pm \frac{\pi }{6}\]
C) \[n\pi \pm \frac{\pi }{6}\]
D) \[2n\pi \pm \frac{\pi }{3}\]
Correct Answer: D
Solution :
\[{{\cos }^{2}}\theta -\frac{5}{2}\cos \theta +1=0\] \[\Rightarrow \] \[\cos \theta =\frac{(5/2)\pm \sqrt{(25/4)-4}}{2}=\frac{5\pm 3}{4}\] Rejecting (+) sign, \[\Rightarrow \] \[\cos \theta =\frac{1}{2}=\cos \left( \frac{\pi }{3} \right)\Rightarrow \theta =2n\pi \pm \frac{\pi }{3}\].
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