The set of values of x, satisfying the equation `tan^(2) ( sin^(-1) x) gt 1 ` is

Options

A. `[-1,1]`
B. `[-(1)/sqrt(2),(1)/sqrt(2)]`
C. `(-1,1)-[-(1)/sqrt(2),(1)/sqrt(2)]`
D. `[-1,1]-(1)/sqrt(2),(1)/sqrt(2)`

Explanation

We have
`tan^(2)(som^(-1)x)gt1`
`rarr tan^(2)(sin^(-1)x)-1)gt0`
`rarr tan (sin^(-1)x)lt-1 or tan (sin^(-1)x)gt1`
`rarr -infty lt tan(sin^(-1)x)lt-1 or 1 lt tan (sin^(-1)x)lt infty`
`rarr -(pi)/(2)ltsin^(-1)xlt(pi)/(2)`
`rarr x in(-1,-(1)/sqrt(2) or x in (1)sqrt(2),1)`
`rarr x in (-1,-1)-[-(1)/sqrt(2)),(1)/sqrt(2)]`