A) \[\frac{13\pi }{6}\]
B) \[\pi \]
C) \[2\pi \]
D) \[\frac{5\pi }{3}\]
Correct Answer: C
Solution :
\[2\left( 1-{{\sin }^{2}}\theta \right)+3\sin \theta =0\] \[\Rightarrow 2{{\sin }^{2}}\theta -3\sin \theta -2=0\] \[\Rightarrow (2\sin \theta +1)(\sin \theta -2)=0\] \[\Rightarrow \sin \theta =-\frac{1}{2};\sin \theta =2(reject)\] roots\[\pi +\frac{\pi }{6},2\pi -\frac{\pi }{6},-\frac{\pi }{6},-\pi +\frac{\pi }{6}\] \[\Rightarrow \]sum of values\[=2\pi \]
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