The value of x that satisfies $tan^{-1}(tan 3)=tan^2x$, is

$\frac{\pi}{3}$ $-\frac{\pi}{3}$ $\sqrt{tan^{-1}3}$ none of these

none of these

We have, $tan^{-1}(tan 3) = tan^{-1}\begin{Bmatrix}tan (3 - \pi )\end{Bmatrix}=  3 - \pi < 0$ and, $tan^2 x ≥ 0$ $∴ tan^{-1}(tan 3) = tan^2 x $ has no solution.