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Mathematics · 2026 · 2 marks
Inverse Trigonometric FunctionsProperties of Inverse Trigonometric Functions2 marksApplyvery short answer
CBSE 2026 · Region 1 · Set 2 · Q25
(a) Simplify: cot^-1 √((1+ cos 2 x)/(1- cos 2 x)), x ∈(0, (π)/2).
(a)
Simplify : $\displaystyle \cot ^{-1} \sqrt{\frac{1+\cos 2 x}{1-\cos 2 x}}, x \in\left(0, \frac{\pi}{2}\right)$.
OR
(b)
Evaluate : $\displaystyle \sin \left(\tan ^{-1}(-\sqrt{3})-\sec ^{-1} 2\right)$
Marking-scheme solution
(a)
Given expression $\displaystyle = \cot^{-1}\left(\sqrt{\dfrac{2\cos^2 x}{2\sin^2 x}}\right)$
$\displaystyle = \cot^{-1}(\cot x) = x$
OR
(b)
Given expression $\displaystyle = \sin\left(-\dfrac{\pi}{3} - \dfrac{\pi}{3}\right)$
$\displaystyle = \sin\left(-\dfrac{2\pi}{3}\right) = -\dfrac{\sqrt3}{2}$
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CBSE Class 12 Mathematics past-paper question from the 2026 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.