Let ${\tan ^{ - 1}}y = {\tan ^{ - 1}}x + {\tan ^{ - 1}}\left( {{{2x} \over {1 - {x^2}}}} \right),$ where $\left| x \right| < {1 \over {\sqrt 3 }}.$ Then a value of $y$ is :

Question

Let ${\tan ^{ - 1}}y = {\tan ^{ - 1}}x + {\tan ^{ - 1}}\left( {{{2x} \over {1 - {x^2}}}} \right),$
where $\left| x \right| < {1 \over {\sqrt 3 }}.$ Then a value of $y$ is :

${{3x - {x^3}} \over {1 + 3{x^2}}}$

${{3x + {x^3}} \over {1 + 3{x^2}}}$

${{3x - {x^3}} \over {1 - 3{x^2}}}$

${{3x + {x^3}} \over {1 - 3{x^2}}}$

Solution

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