The number of solutions of the equation
`|2 sin x-sqrt(3)|^(2 cos^(2) x-3 cos x+1)=1` in `[0, pi]` is

Options

A. 2
B. 3
C. 4
D. 5

Answer

B

Explanation

`|2 sin x -sqrt(3)|^()=1`
Case I : `2 cos^(2) x-3 cos x+1 =0`
`cos x=1/2, 1`
`x=0, pi/3`
But at `x=pi/3, L.H.S. =0^(@)`
`:. x=pi/3` (rejected)
`:. x=0` is a solution
Case II : `2 sin x-sqrt(3) =1, -1`
`:. sin x=(sqrt(3)+1)/2, (sqrt(3)-1)/2`
`sin x=(sqrt(3)-1)/2`
`:.` x has 2 values in `[0, pi]`
`:.` Total number of solutons `=2+1=3`