A) \[2n\pi \pm {{\cos }^{-1}}\frac{-3+\sqrt{17}}{4}\]
B) \[2n\pi \pm {{\cos }^{-1}}\frac{-3-\sqrt{17}}{4}\]
C) \[n\pi \pm {{\cos }^{-1}}\frac{-3+\sqrt{17}}{4}\]
D) \[n\pi \pm {{\cos }^{-1}}\frac{-3-\sqrt{17}}{4}\]
Correct Answer: A
Solution :
\[2{{\cos }^{2}}\theta -1+3\cos \theta =0\] \[\cos \theta =\frac{-3\pm \sqrt{9+8}}{4}=\frac{-3\pm \sqrt{17}}{4}\] \[\Rightarrow \] \[\theta =2n\pi \pm {{\cos }^{-1}}\left( \frac{-3+\sqrt{17}}{4} \right)\], (Taking +ve sign).
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