If z = `sec^(-1) (x + 1/x) + sec^(-1) (y + 1/y)`, where xy< 0, then the possible value of z is (are)

Options

A. `(8pi)/(10)`
B. `(7pi)/(10)`
C. `(9pi)/(10)`
D. `(21pi)/(20)`

Answer

C, D

Explanation

`xy lt 0`
`rArr x + (1)/(x) ge 2, y + (1)/(y) le -2`
or `x + (1)/(x) le -2, y + (1)/(y) ge 2`
`x + (1)/(x) ge 2`
`rArr sec^(-1) (x + (1)/(x)) in [(pi)/(3), (pi)/(2))`
`y + (1)/(y) le -2`
`rArr sec^(-1) (y + (1)/(y)) in ((pi)/(2), (2pi)/(3)]`
`rArr z in ((5pi)/(6), (7pi)/(6))`