If `|cos^-1((1-x^2)/(1+x^2))| < pi/3,` then x belongs to the intervalA. `[-1//sqrt(3),1//sqrt(3)]`B. `(-1//sqrt(3),1//sqrt(3))`C. `(0,1//sqrt(3))`D. none of these

If `|cos^-1((1-x^2)/(1+x^2))| < pi/3,` then x belongs to the intervalA

1.	If `\|cos^-1((1-x^2)/(1+x^2))\| < pi/3,` then x belongs to the intervalA. `[-1//sqrt(3),1//sqrt(3)]`B. `(-1//sqrt(3),1//sqrt(3))`C. `(0,1//sqrt(3))`D. none of these
Answer» We have `\|cos^(-1)((1-x^(2))/(1+x^(2)))\|lt(pi)/(3)` ltrbgt `rarr 1/2 lt (1-x^(2))/(1+x^(2)) lt (pi)/(3)` `rarr 1+x^(2)lt2-2x^(2)lt2+2x^(2)` `rarr 1+x^(2)lt2-2x^(2) and 2-2x^(2)lt2+2x^(2)` `rarr 3x^(2)-1lt0and 4x^(2)gt0 rarr -(1)sqrt(3)ltxlt(1)/sqrt(3)`

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