The value of
Question:

The value of $\cot \left(\tan ^{-1} x+\cot ^{-1} x\right)$ for all $x \in R$, is ____________________

Solution:

We know

$\tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2}$, for all $x \in \mathrm{R}$

$\therefore \cot \left(\tan ^{-1} x+\cot ^{-1} x\right)=\cot \frac{\pi}{2}$

$\Rightarrow \cot \left(\tan ^{-1} x+\cot ^{-1} x\right)=0$

The value of $\cot \left(\tan ^{-1} x+\cot ^{-1} x\right)$ for all $x \in \mathrm{R}$, is __0__.