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

Monjur Alahi

If `tan^(-1)(sqrt(1+x^2-1))/x=4^0` then `x=tan2^0` (b) `x=tan4^0` `x=tan1/4^0` (d) `x=tan8^0`
A. `x = tan 2^(@)`
B. `x = tan 4^(@)`
C. `x = tan (1//4)^(@)`
D. `x = tan 8^(@)`


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Correct Answer - D
`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^(@)`

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