A) \[n\pi +{{(-1)}^{n+1}}\frac{\pi }{6}\]
B) \[n\pi +{{(-1)}^{n}}\frac{\pi }{2}\]
C) \[n\pi +{{(-1)}^{n}}\frac{5\pi }{6}\]
D) \[n\pi +{{(-1)}^{n}}\frac{7\pi }{6}\]
Correct Answer: A
Solution :
\[2{{\sin }^{2}}\theta -3\sin \theta -2=0\] \[\Rightarrow \]\[(2\sin \theta +1)(\sin \theta -2)=0\] \[\Rightarrow \] \[\sin \theta =-\frac{1}{2}\] \[[\because \sin \theta \ne 2]\] \[\Rightarrow \]\[\sin \theta =\sin \left( -\frac{\pi }{6} \right)\Rightarrow \theta =n\pi +{{(-1)}^{n}}\left[ -\frac{\pi }{6} \right]\] \[\Rightarrow \]\[n\pi +{{(-1)}^{n+1}}\frac{\pi }{6}\]
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