question_answer

The number of values of x in the interval \[[0,\,3\pi ]\] satisfying the equation \[2{{\sin }^{2}}x+5\sin x-3=0\] is

A) 4                     

B)   6

C) 1                     

D)   2

Correct Answer: A

Solution :

\[(\sin x+3)\,(2\sin x-1)=0\] \[\Rightarrow \,\,\sin x=\frac{1}{2}\] and \[\sin x\ne -3\] \[\therefore \,\]  In \[\left[ 0,3\pi  \right],\] x has 4 values.