Evaluate : - ^ -1 (-1 3 )+ ^ -1 (1 3 )+ ^ -1 ( (- 2 ) ) - Vidyadip

Question

Evaluate : $- \tan ^{-1}\left(-\frac{1}{\sqrt{3}}\right)+\cot ^{-1}\left(\frac{1}{\sqrt{3}}\right)+\tan ^{-1}\left(\sin \left(-\frac{\pi}{2}\right)\right)$

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Answer

$\tan ^{-1}\left(-\frac{1}{\sqrt{3}}\right)+\cot ^{-1}\left(\frac{1}{\sqrt{3}}\right)+\tan ^{-1}\left(\sin \left(-\frac{\pi}{2}\right)\right)$
$=-\frac{\pi}{6}+\frac{\pi}{3}+\tan ^{-1}(-1)$
$=-\frac{\pi}{6}+\frac{\pi}{3}-\frac{\pi}{4}$
$=-\frac{\pi}{12}$

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