A) \[n\pi +{{(-1)}^{n}}\frac{\pi }{6}\]
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: D
Solution :
\[2{{\sin }^{2}}\theta -3\sin \theta -2=0\]\[\Rightarrow \] \[(2\sin \theta +1)\,\,(\sin \theta -2)=0\] \[\Rightarrow \] \[\sin \theta =-\frac{1}{2}\] , (\[\because \,\sin \theta \ne 2)\]\[\Rightarrow \] \[\sin \theta =\sin \left( \frac{-\pi }{6} \right)\] \[\Rightarrow \] \[\theta =n\pi +{{(-1)}^{n}}\left( \frac{-\pi }{6} \right)\Rightarrow \theta =n\pi +{{(-1)}^{n+1}}\frac{\pi }{6}\] \[\Rightarrow \] \[\theta =n\pi +{{(-1)}^{n}}\frac{7\pi }{6}\], \[\left\{ \because \,\,\frac{-\pi }{6}\text{is equivalent to }\frac{7\pi }{6} \right\}\].
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