Find the principal value of `sec^(-1)(2/sqrt3)`

Options

A. `pi/3, (11 pi)/6`
B. `pi/6, (11 pi)/6`
C. `pi/6, (11pi)/4`
D. `pi/6, (11pi)/4`

Answer

B

Explanation

Given, ` sec x = 2/sqrt3 `
` :. " " sec x = sec (pi/6)`
` sec x = sec (2pi - pi/6)`
` = sec ((11 pi)/6)`
such that ` 0 lt pi/6 lt 2 pi and 0 lt (11 pi)/6 lt 2 pi `.
` :. ` Principal solutions are ` x = pi/6 and x = (11 pi)/6`
Hence, the correct answer from the given alternatives is (b) .