`f(x)=tan^(-1)x+tan^(-1)(1/x);g(x)=sin^(-1)x+cos^(-1)x` are identical functions if (A)`x in R` (B) `x >0` (C) `x in [-1,1]` (D) `x in (0,1]`

Options

A. `x in R`
B. `x gt 0`
C. `x in [-1, 1]`
D. `x in (0,1]`

Answer

D

Explanation

`f(x) = tan^(-1) x + tan^(-1).(1)/(x) = {((pi)/(2),x gt 0),((-pi)/(2),x lt 0):}`
`g(x) = sin^(-1) x + cos^(-1) x = (pi)/(2) AA x in [-1, 1]`
Therefore, common domain is `x in (0, 1]`