The complete solution set of the inequality `(cos^(-1)x)^(2)-(sin^(-1)x)^(2) gt 0` is :

Options

A. `[0,(1)/sqrt(2))`
B. `[-1,(1)/sqrt(2))`
C. `[-1,sqrt(2))`
D. None of these

Answer

B

Explanation

Given, `(cos^(-1)x)^(2)-(sin^(-1)x)^(2)gt0`
`ltimplies(cos^(-1)x+sin^(-1)x)(cos^(-1)x-sin^(-1)x)gt0`
`ltimplies(pi)/(2)(cos^(-1)x sin^(-1) x)gt 0`
`ltimplies cos^(-1)x-sin^(-1)x gt 0`
`ltimplies (pi)/(2)-2sin^(-1)xgt0 ltimplies -1le x lt (1)/sqrt(2)`
`[ because "for" cos^(-1) x "and" sin^(-1) x "to be defined" -1 le x le 1 ]`