If `a le sin^(-1)x +cos^(-1)x+tan^(-1)x le b`, then:

Options

A. `alpha=(pi)/(4),beta =(3pi)/(4)`
B. `alpha=-pi, beta=2pi`
C. `alpha=0, beta=pi`
D. none of these

Explanation

We have
`sin^(-1)x+cos^(-1)x=(pi)/(2)` for all `x in [-1,1]`
Also
`-(pi)/(4)le tan x le(pi)/(4)` for all `x in [-1,1]`
`therefore -(pi)/(4)+(pi)/(2)lesin^(-1)x+cos^(-1)x+tan^(-1)xle(pi)/(41)+(pi)/(2)`
`rarr (pi)/(4)lesin^(-1)x+cos^(-1)x+tan^(-1)xle(3pi)/(4)`