A) 0
B) 5
C) 6
D) 10
Correct Answer: C
Solution :
Given,\[3{{\sin }^{2}}x-7\sin x+2=0\] \[\Rightarrow \]\[(2\sin x-1)(\sin x-2)=0\] \[\Rightarrow \]\[\sin x=\frac{1}{3}\] \[(\because \,\,\sin x\ne 2)\] Let\[{{\sin }^{-1}}\frac{1}{3}=\alpha ,\,\,0<\alpha <\frac{\pi }{2}\]are the solutions in\[[0,\,\,5\pi ]\]. Then, \[\alpha ,\,\,\pi -\alpha ,\,\,2\pi +\alpha ,\,\,3\pi -\alpha ,\,\,4\pi +\alpha ,\,\,5\pi -\alpha \]are the solutions.
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