Number of roots of `cos^2x+(sqrt(3)+1)/2sinx-(sqrt(3))/4-1=0` which lie in the interval `[-pi,pi]` is 2 (b) 4 (c) 6 (d) 8

Options

A. 2
B. 4
C. 6
D. 8

Answer

B

Explanation

`1- sin^(2) x+ (sqrt(3)+1)/2 sin x -sqrt(3)/4-1=0`
or `sin^(2) x-(sqrt(3)+1)/2 sin x + sqrt(3)/4=0`
or `4 sin^(2) x-2 sqrt*3) sin x -2 sin x + sqrt(3)=0`
On solving, we get `sin x=1//2, sqrt(3)//2`
`rArr x=pi//6, 5 pi//6, pi//3, 2 pi//3`