Find the principal value of each of the following : sec^-1(-2/√3)

Question

Find the principal value of each of the following :

\(\sec^{-1}\left(\frac{-2}{\sqrt{3}}\right)\)

Answer 1

\(\sec^{-1}\left(\frac{-2}{\sqrt{3}}\right)\)\(=\pi-\sec^{-1}\left(\frac{2}{\sqrt{3}}\right)\)

[ Formula: sec ^-1(-x)= π – sec ^-1(x) ]

\(=\pi-\frac{\pi}{6}=\frac{5\pi}{6}\)