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

Question

$\begin{array}{1 1} \frac{3x+x^3}{1-3x^2} \\ \frac{3x-x^3}{1+3x^2} \\ \frac{3x+x^3}{1+3x^2} \\ \frac{3x-x^3}{1-3x^2} \end{array} $