Question

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

Answer 1

We know that ${\cot }^{-1}\left(-x\right)=\mathrm{\pi }-{\cot }^{-1}\left(x\right)$
Therefore, the value of ${\cot }^{-1}\left(-x\right)$ for all $x\in R$ in terms of ${\cot }^{-1}x$ is $\mathrm{\pi }-{\cot }^{-1}\left(x\right)$.