If `|cos^(-1)((1-x^2)/(1+x^2))|

1.	If `\|cos^(-1)((1-x^2)/(1+x^2))\|
Answer» `\|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).` So, option `c` is the correct option.

Discussion

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