If `log_(2)xge0` then `log_(1//pi){sin^(-1)((2x)/(1+x^(2)))+2tan^(-1)x}` is equal

Options

A. `log_(1//pi)(4 tan^(-1)x)`
B. 0
C. `-1`
D. none of these

Explanation

We have
`log_(2) xge 0rarr xge 2^(@)=1`
for `xge1` we have
`sin^(-1)(2x)/(1+x^(2))=pi-2 tan^(-1)x`
`therefore log_(1//pi){sin^(-1)(2x)/(1+x^(2))+2 tan^(-1)x}`
`=log_(1//pi)(pi-2tan^(-1)x+2 tan ^(-1)x)`
`=log_(1//pi) pi=-1`