CBSE 2026 · Region 1 · Set 2 · Q25 · 2 marks
Simplify : $\displaystyle \cot ^{-1} \sqrt{\frac{1+\cos 2 x}{1-\cos 2 x}}, x \in\left(0, \frac{\pi}{2}\right)$.Evaluate : $\displaystyle \sin \left(\tan ^{-1}(-\sqrt{3})-\sec ^{-1} 2\right)$
Simplify : $\displaystyle \cot ^{-1} \sqrt{\frac{1+\cos 2 x}{1-\cos 2 x}}, x \in\left(0, \frac{\pi}{2}\right)$.
Evaluate : $\displaystyle \sin \left(\tan ^{-1}(-\sqrt{3})-\sec ^{-1} 2\right)$
Marking-scheme solution
Given expression $\displaystyle = \cot^{-1}\left(\sqrt{\dfrac{2\cos^2 x}{2\sin^2 x}}\right)$
$\displaystyle = \cot^{-1}(\cot x) = x$
Given expression $\displaystyle = \sin\left(-\dfrac{\pi}{3} - \dfrac{\pi}{3}\right)$
$\displaystyle = \sin\left(-\dfrac{2\pi}{3}\right) = -\dfrac{\sqrt3}{2}$
Inverse Trigonometric FunctionsProperties of Inverse Trigonometric FunctionsApplyvery_short_answermedium
More from Inverse Trigonometric Functions
- The principal value of cot^-1(-1/(√3)) is:2025 · asked 3×
- Evaluate sin^-1( sin (3 π)/4)+ cos^-1( cos π)+ tan^-1(1) OR Draw the graph of cos^-1 x, where x ∈[-1,0].…2023 · asked 3×
- The principal value of sec^-1(√2)+2 cosec^-1(-√2) is:2026 · asked 3×
- Assertion: Maximum value of ( cos^-1 x)^2 is π^2. Reason (R): Range of the principal value branch of cos^-1 x…2023 · asked 3×
- If a function f: X → Y defined as f(x)=y is one-one and onto, then we can define a unique function g: Y → X…2024 · asked 3×
- Simplify sin^-1( x√1+x^2). OR Find domain of sin^-1 √x-1.2025 · asked 3×
- Domain of f(x)= cos^-1 x+ sin x is:2025 · asked 3×
- Assertion: Domain of y= cos^-1(x) is [-1,1]. Reason (R): The range of the principal value branch of y=…2024 · asked 3×
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.