Question

Find the principal value of the following:

cot^-1 (- √3)

Answer 1

Let cot^-1 (- √3) = x ⇒ cot x = - √3

⇒ cot x = - cot \(\frac{\pi}{3}\) ⇒ cot x = cot (π - \(\frac{\pi}{3}\))

⇒ cot x = cot  \(\frac{2\pi}{3}\)

We know that the range of the principal value of cot^-1 x is (0, π) and cot (\(\frac{2\pi}{3}\)) = - √3

Thus, the principal value of cot^-1 (- √3) is \(\frac{2\pi}{3}\).