Number of solutions of the equation `4(cos^(2) 2x+ cos 2 x +1)+tan x (tan x-2sqrt(3))=0` in `[0, 2pi]` is

Options

A. 0
B. 1
C. 2
D. 3

Answer

C

Explanation

`(4 cos^(2) 2x+4 cos 2x+1) + (tan^(2) x-2 sqrt(3) tan x+3)=0`
`rArr (2 cos 2x+1)^(2) + (tan x-sqrt(3))^(2)=0`
`rArr cos 2x = -1/2 and tan x = sqrt(3)`
`rArr 2 cos^(2) x-1=-1/2 and tan x=sqrt(3)`
`rArr cos x = pm 1/2 and tan x = sqrt(3)`
`rArr x=pi/3, (4pi)/3`
`:.` Number of solution of equation `=2`