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__.
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