The least positive solution of `cot (pi/(3 sqrt(3)) sin 2x)=sqrt(3)` lies in

Options

A. `(0, pi/6]`
B. `(pi/9, pi/6)`
C. `(pi/12, pi/9]`
D. `(pi/3, pi/2]`

Answer

A

Explanation

`cot (pi/(3sqrt(3)) sin 2 x)=sqrt(3)`
`rArr pi/(3sqrt(3)) sin 2x=n pi +pi/6, n in Z`
`rArr sin 2x=3sqrt(3) n + sqrt(3)/2`
For solution, `n=0`
`rArr sin 2x=sqrt(3)/2`
`rArr 2x=pi/3 rArr x=pi/6`