If `cot x + cosec x = sqrt(3)x`, then the principal value of `(x-(pi)/(6))` is

Options

A. `(pi)/(3)`
B. `(pi)/(4)`
C. `(pi)/(2)`
D. `(pi)/(6)`

Answer

D

Explanation

Given , `cot x + cosec x = sqrt(3)`
`rArr (cos x +1)/(sinx) = sqrt(3)`
`rArr (2cos^(2)""(x)/(2))/(2 sin""(x)/(2)cos""(x)/(2))=sqrt(3)`
`rArr tan""(x)/(2) = (1)/(sqrt(3))`
`therefore (x)/(2) = npi+(pi)/(6)`
`rArr x-(pi)/(6) =2npi+(pi)/(6)`
For n = 0, principal value of
`x - (pi)/(6) " is" (pi)/(6).`