complete solution set of `tan^(-1) (sin^(-1) x) gt 1` is

Options

A. `(-1, -(1)/(sqrt2)) uu ((1)/(sqrt2), 1)`
B. `(-(1)/(sqrt2), (1)/(sqrt2)) ~ {0}`
C. `(-1, 1) ~ {0}`
D. none of these

Answer

A

Explanation

`[tan (sin^(-1) x)]^(2) gt 1`
`rArr tan (sin^(-1) x) lt -1 " or" tan (sin^(-1) x) gt 1`
`rArr (pi)/(4) lt sin^(-1) x lt (pi)/(2) " or " -(pi)/(2) lt sin^(-1) x lt -(pi)/(4)`
`rArr x in ((1)/(sqrt2), 1) " or " x in (-1, (1)/(sqrt2))`
`rArr x in (-1, -(1)/(sqrt2)) uu ((1)/(sqrt2), 1)`