The principal value of cot-1(-1) isA. \(\frac{-\pi}{4}\)B. \(\frac{\

1.	The principal value of cot-1(-1) isA. \(\frac{-\pi}{4}\)B. \(\frac{\pi}{4}\)C. \(\frac{5\pi}{4}\)D. \(\frac{3\pi}{4}\)
Answer» 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 =\(\frac{3\pi}{4}\)

The principal value of cot-1(-1) isA. \(\frac{-\pi}{4}\)B. \(\frac{\pi}{4}\)C. \(\frac{5\pi}{4}\)D. \(\frac{3\pi}{4}\)

Answer»

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 =\(\frac{3\pi}{4}\)