Find the principal value of each of the following :\(\tan^{-1}\left(\t

1.	Find the principal value of each of the following :\(\tan^{-1}\left(\tan\frac{7\pi}{6}\right)\)
Answer» \(\tan^{-1}\left(\tan\frac{7\pi}{6}\right)\)\(=\tan^{-1}\left(\tan\left(\pi+\frac{\pi}{6}\right)\right)\) [ 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 ] \(=\frac{\pi}{6}\)

Find the principal value of each of the following :\(\tan^{-1}\left(\tan\frac{7\pi}{6}\right)\)

Answer»

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

[ 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 ]

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