If `tan^(-1)((sqrt(1+x^2)-1)/x)=4^0` then (a)`x=tan2^0` (b) `x=tan4^0` (c)`x=tan1/4^0` (d) `x=tan8^0`

Options

A. `x = tan 2^(@)`
B. `x = tan 4^(@)`
C. `x = tan (1//4)^(@)`
D. `x = tan 8^(@)`

Answer

D

Explanation

`tan^(-1). (sqrt(1 + x^(2)) -1)/(x) = 4^(@) " " (x != 0)`
`rArr (sqrt(1 + x^(2)) -1)/(x) = tan4^(@)`
`rArr sqrt(1 + x^(2)) = 1 + x tan 4^(@)`
`rArr 1 + x^(2) = 2x tan 4^(@) + 1 + x^(2) tan^(2) 4^(@)`
`rArr x = 0 " or " x = (2 tan 4^(@))/(1 - tan^(2) 4^(@)) = tan 8^(@)`
Since `x != 0`, we have `x = tan 8^(@)`