If `2 tan^(-1)x= sin^(-1)K` then the value of k is

Options

A. `pi//2`
B. `pi`
C. `2pi`
D. `3pi`

Answer

C

Explanation

`f(x)={{:(sin^(-1)x+cos^(-1)x,,0le x le 1),(cos^(-1)x-sin^(-1)x,,-1le x le x lt 0):}`
`f(x)={{:(pi//2",",0le x le 1),((pi)/(2)-2sin^(1)x",",-1le x lt 0):}`
For `-1 le x le 0`
`-pi//2 le sin^(-1)x le 0`
`therefore -pi le 2 sin^(-1)x le 0`
`therefore 0 le -2 sin^(-1)x le pi`
`therefore pi//2 le pi//2 -2 sin^(-1) x le 3pi//2`
`therefore` Max. value `= 3pi//2`
and Min. value `= pi//2`