Question:
The value of $\cot ^{-1}(-x)$ for all $x \in R$ in terms of $\cot ^{-1} x$ is _________________.
Solution:
We know
$\cot ^{-1}(-x)=\pi-\cot ^{-1} x$, for all $x \in \mathrm{R}$
The value of $\cot ^{-1}(-x)$ for all $x \in \mathrm{R}$ in terms of $\cot ^{-1} x$ is $\pi-\cot ^{-1} x$