Find the value of

Question:

Find the value of tan-1 (-1/√3) + cot-1(1/√3) + tan-1(sin (-π/2))

Solution:

Given,

tan-1 (-1/√3) + cot-1(1/√3) + tan-1(sin (-π/2))

$=\tan ^{-1}\left(\tan \left(-\frac{\pi}{6}\right)\right)+\cot ^{-1}\left(\cot \frac{\pi}{3}\right)+\tan ^{-1}(-1)$

$=-\frac{\pi}{6}+\frac{\pi}{3}+\left(-\frac{\pi}{4}\right)=-\frac{\pi}{12}$

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