The principal value of cot^-1(-√3) is

Question

The principal value \(cot^{-1}(-\sqrt{3})\) of 

A. \(\frac{2\pi}{6}\)

B. \(\frac{\pi}{6}\)

C. \(\frac{7\pi}{6}\)

D. \(\frac{5\pi}{6}\)

Answer 1

To Find: The Principle value of \(cot^{-1}(-\sqrt{3})\)

Let the principle value be given by x 

Now, let x = \(cot^{-1}(-\sqrt{3})\)

⇒ cot x = \(-\sqrt{3}\)

⇒ cot x= - cot( \(\frac{\pi}{6}\)) ( \(\because -cot\left(\frac{\pi}{6}\right)=\sqrt{3}\) ) 

⇒ cot x=cot( \(\pi-\frac{\pi}{6}\)) ( \(\because -cot(\theta)=cot(\pi-\theta\))) 

⇒ x =\(\frac{5\pi}{6}\)