If `|cos^(-1)((1-x^2)/(1+x^2))| < pi/3,t h e n` (a) `x in [-1/3,1/(sqrt(3))]` (b) `x in [-1/(sqrt(3)),1/(sqrt(3))]` `x in [0,1/(sqrt(3))]` (d) none of these

Explanation

`|cos^-1((1-x^2)/(1+x^2))| lt pi/3`

`=> - pi/3 lt cos^-1((1-x^2)/(1+x^2)) lt pi/3`

we know, range of `cos^-1y` is from `0` to `pi`.

`:. 0 le cos^-1((1-x^2)/(1+x^2)) lt pi/3`

`=> 1/2 lt (1-x^2)/(1+x^2) le 1`

`=> 1+x^2 lt 2-2x^2 le 2+2x^2`

`=> 0 le x^2 lt 1/3`

`=> :. x in (-1/sqrt3,1/sqrt3).`

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