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

1.	Find the principal value of each of the following :\(\tan^{-1}\left(\tan\frac{3\pi}{4}\right)\)
Answer» \(\tan^{-1}\left(\tan\frac{3\pi}{4}\right)=tan^{-1}\left(\tan\left(\pi-\frac{\pi}{4}\right)\right)\) [Formula: tan(π – x) = -tan (x) , as tan is negative in the second quadrant. ] \(=\tan^{-1}\left(-\tan\frac{\pi}{4}\right)\) [Formula: tan^-1(tan x) = x ] =\(-\frac{\pi}{4}\)

Find the principal value of each of the following :\(\tan^{-1}\left(\tan\frac{3\pi}{4}\right)\)

Answer»

\(\tan^{-1}\left(\tan\frac{3\pi}{4}\right)=tan^{-1}\left(\tan\left(\pi-\frac{\pi}{4}\right)\right)\)

[Formula: tan(π – x) = -tan (x) , as tan is negative in the second quadrant. ]

\(=\tan^{-1}\left(-\tan\frac{\pi}{4}\right)\)

[Formula: tan^-1(tan x) = x ]

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