A) 0
B) 5
C) 6
D) 10
Correct Answer: C
Solution :
\[3{{\sin }^{2}}x-7\sin x-\sin x+2=0\] \[\Rightarrow \] \[3{{\sin }^{2}}x-6\sin x-\sin x+2=0\] \[\Rightarrow \] \[3\sin x(\sin x-2)-1(\sin x-2)=0\] \[\Rightarrow \] \[\sin x=\frac{1}{3}\]or \[2\] \[\Rightarrow \] \[\sin x=\frac{1}{3}\] \[[\because \sin x\ne 2]\] Let \[{{\sin }^{-1}}\frac{1}{3}=\alpha ,0<\alpha <\frac{\pi }{2}\] then\[\alpha ,\pi -\alpha ,2\pi +\alpha ,3\pi -\alpha ,\] \[4\pi +\alpha +5\pi -\alpha \]are the solution in \[[0,5\pi ]\] \[\therefore \]Required number of solution\[=6\]You need to login to perform this action.
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