question_answer

The number of values of\[x\]in the interval \[[0,3\pi ]\]satisfying the equation \[2\text{ }si{{n}^{2}}x+5\text{ }sin\text{ }x-3=0\]is     AIEEE  Solved  Paper-2006

A) 6                             

B)        1                             

C)        2                             

D)        4

Correct Answer: D

Solution :

Since,   \[2\text{ }{{\sin }^{2}}x+5\sin x-3=0\] \[\Rightarrow \] \[(2\sin \,x-1)(\sin \,x+3)=0\] \[\Rightarrow \] \[\sin x=1/2\]                   \[(\because \sin x\ne -3)\] From figure, it is clear that the number of intersection points of\[y=\frac{1}{2}\]and\[y=sinx\]is 4. Hence, solutions of given equation in\[[0,3\pi ]\]is 4.