Find the principal value of each of the following : tan^-1(tan 7π/6)

Question

Find the principal value of each of the following :

\(\tan^{-1}\left(\tan\frac{7\pi}{6}\right)\)

Answer 1

\(\tan^{-1}\left(\tan\frac{7\pi}{6}\right)\)\(=\tan^{-1}\left(\tan\left(\pi+\frac{\pi}{6}\right)\right)\)

[ Formula: tan( π + x) = tan x, as tan is positive in the third quadrant.]

\(=\tan^{-1}\left(\tan\frac{\pi}{6}\right)\) [Formula: tan ^-1(tan x) = x ]

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