What is the principle value of `sec^(-1)((2)/(sqrt(3)))` ?

Options

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

Answer

D

Explanation

Let `sec^(-1)((2)/(sqrt(3)))="y where 0" lt y le (pi)/(2)`
`rArr sec y = (2)/(sqrt(3))`
`rArr sec y = "sec"(pi)/(6) rArr y = (pi)/(6)`
`therefore" ""The principal value of" sec^(-1)((2)/(sqrt(3)))=(pi)/(6)`