Write the value
Question:

Write the value of $\cot ^{-1}(-x)$ for all $x \in R$ in terms of $\cot ^{-1} x$

Solution:

We know that $\cot ^{-1}(-x)=\pi-\cot ^{-1}(x)$

Therefore, the value of $\cot ^{-1}(-x)$ for all $x \in R$ in terms of $\cot ^{-1} x$ is $\pi-\cot ^{-1}(x)$.