CBSE 2026 · Region 4 · Set 1 · Q21 · 2 marks
Evaluate: \[\tan ^{-1}\left(-\frac{1}{\sqrt{3}}\right)+\cot ^{-1}\left(\frac{1}{\sqrt{3}}\right)+\tan ^{-1}\left(\sin \left(-\frac{\pi}{2}\right)\right)+\tan ^{-1}\left(\tan \frac{2 \pi}{3}\right) \]
Marking-scheme solution
$\displaystyle \tan^{-1}\left(\dfrac{-1}{\sqrt{3}}\right)+\cot^{-1}\left(\dfrac{1}{\sqrt{3}}\right)+\tan^{-1}\left(\sin\left(\dfrac{-\pi}{2}\right)\right)+\tan^{-1}\left(\tan \dfrac{2 \pi}{3}\right)$
$\displaystyle =-\dfrac{\pi}{6}+\dfrac{\pi}{3}-\dfrac{\pi}{4}-\dfrac{\pi}{3}$
$\displaystyle =\dfrac{-5 \pi}{12}$
Inverse Trigonometric FunctionsProperties of Inverse Trigonometric FunctionsApplyvery_short_answermedium
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CBSE Class 12 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.