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The least positive solution of cot(pi/(...

The least positive solution of `cot(pi/(3sqrt3) sin2x)=sqrt3` lie (a) `(0,pi/6]` (b) `(pi/9,pi/6)` (c) `(pi/12,pi/9)` (d) `(pi/3,pi/2)`

A

`(0, pi/6]`

B

`(pi/9, pi/6)`

C

`(pi/12, pi/9]`

D

`(pi/3, pi/2]`

Text Solution

Verified by Experts

The correct Answer is:
A
`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`
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