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f(x)=tan^(-1)x+tan^(-1)(1/x);g(x)=sin^(-...

`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 gt 0`

C

`x in [-1, 1]`

D

`x in (0,1]`

Text Solution

Verified by Experts

The correct Answer is:
D
`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]`
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