The principal value of sec^-1(-2/√3) is

Question

The principal value of \(sec^{-1}\left(\frac{-2}{\sqrt{3}}\right)\)is

A. \(\frac{\pi}{6}\)

B. \(\frac{-\pi}{6}\)

C. \(\frac{5\pi}{6}\)

D. \(\frac{7\pi}{6}\)

Answer 1

Correct Answer is \(\frac{5\pi}{6}\)

Let the principle value be given by x 

Now, let x = \(sec^{-1}\left(\frac{-2}{\sqrt{3}}\right)\)

⇒ sec x = \(\frac{-2}{\sqrt{3}}\)

⇒ sec x= - sec( \(\frac{\pi}{6}\)) ( \(\because sec\left(\frac{\pi}{6}\right)=\left(\frac{2}{\sqrt{3}}\right)\)

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

⇒ x =\(\frac{5\pi}{6}\)