A) \[n\pi \pm \frac{\pi }{3}\]
B) \[2n\pi \pm \frac{\pi }{3}\]
C) \[2n\pi \pm \frac{\pi }{6}\]
D) \[n\pi \pm \frac{\pi }{6}\]
Correct Answer: B
Solution :
\[1-{{\cos }^{2}}\theta -2\cos \theta +\frac{1}{4}=0\] \[\Rightarrow \] \[{{\cos }^{2}}\theta +2\cos \theta -\frac{5}{4}=0\] \[\Rightarrow \] \[\cos \theta =\frac{-2\pm \sqrt{4+5}}{2}=-1\pm \frac{3}{2}\] Since\[|\cos \theta |\,\le 1\], hence \[\cos \theta =-1-\frac{3}{2}\] is ruled out. \[\Rightarrow \] \[\cos \theta =-1+\frac{3}{2}=\frac{1}{2}=\cos \left( \frac{\pi }{3} \right)\]\[\Rightarrow \] \[\theta =2n\pi \pm \frac{\pi }{3}\].
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