Find the principal values of cot^{-1}(-\sqrt{3})

Given cot^-1 \( (-\sqrt{3})\)

Let y = cot^-1 \( (-\sqrt{3})\)

\( – Cot (\dfrac{\pi}{6}) = (\sqrt{3})\)

= \( Cot (π – \dfrac{\pi}{6})\)

= \( cot (\dfrac{5\pi}{6})\)

The range of principal value of cot^-1 is (0, π) and  \(cot (\dfrac{5\pi}{6}) = -\sqrt{3}\)

Thus, the principal value of cot^-1 \( (-\sqrt{3})\) is \( \dfrac{5\pi}{6}\)