If 3tan^-1x+cot^-1x=π , then x equals to :

The correct answer is option (2) → 1

$3\tan^{-1}x+\cot^{-1}x=\pi$

$⇒2\tan^{-1}x+\frac{\pi}{2}=\pi$

so $2\tan^{-1}x=\frac{\pi}{2}$

so $\tan^{-1}x=\frac{\pi}{4}$

$⇒x=1$