Question

The principal value of cot^-1(-1) is

A. \(\frac{-\pi}{4}\)

B. \(\frac{\pi}{4}\)

C. \(\frac{5\pi}{4}\)

D. \(\frac{3\pi}{4}\)

Answer 1

Correct Answer is \(\frac{3\pi}{4}\)

Let the principle value be given by x 

Now, let x = \(cot^{-1}(-1)\)

⇒cot x =-1 

⇒cot x= - cot( \(\frac{\pi}{4}\)) ( \(\because cot\left(\frac{\pi}{4}\right)\))=1) 

⇒cot x=cot( \(\pi-\frac{\pi}{4}\)) ( \(\because -cot(\theta)=cot(\pi-\theta\))) 

⇒x =\(\frac{3\pi}{4}\)