MathematicsMedium66×since 2002Q4088Let tan−1y=tan−1x+tan−1(2x1−x2),{\tan ^{ - 1}}y = {\tan ^{ - 1}}x + {\tan ^{ - 1}}\left( {{{2x} \over {1 - {x^2}}}} \right),tan−1y=tan−1x+tan−1(1−x22x), where ∣x∣<13.\left| x \right| < {1 \over {\sqrt 3 }}.∣x∣<31. Then a value of yyy is :A3x−x31+3x2{{3x - {x^3}} \over {1 + 3{x^2}}}1+3x23x−x3B3x+x31+3x2{{3x + {x^3}} \over {1 + 3{x^2}}}1+3x23x+x3C3x−x31−3x2{{3x - {x^3}} \over {1 - 3{x^2}}}1−3x23x−x3D3x+x31−3x2{{3x + {x^3}} \over {1 - 3{x^2}}}1−3x23x+x3Check answerSkip