Inverse Trigonometric Functions in past papers.

CBSE Board Examination 2026

• Board 2026 Q1Range of $y$ when $2\cos^{-1}x = y$
  Principal value branch of cos⁻¹x1 mark
• Board 2026 Q25Simplify $\tan^{-1}\frac{\cos 2x - \sin 2x}{\cos 2x + \sin 2x}$⁠, or evaluate $\tan\left(\sin^{-1}1 - \cos^{-1}\left(-\frac12\right)\right)$
  Inverse trig functions: simplify, evaluate2 marks

CBSE Board Examination 2025

• Board 2025 Q18Graph of the inverse of the cosine graph
  Graph of cos⁻¹x1 mark
• Board 2025 Q22Evaluate $\tan^{-1}\left[2\sin\left(2\cos^{-1}\frac{\sqrt3}{2}\right)\right]$
  Inverse trigonometric functions: principal values2 marks

CBSE Board Examination 2024

• Board 2024 Q38Case study: the inverse of the sine function
  Inverse sine: branches, value, graph, domain4 marks

CBSE Board Examination 2023

• Board 2023 Q19Range of $2\sin^{-1}x + \frac{3\pi}{2}$
  Range of inverse trigonometric functions1 mark

CBSE Sample Paper 2026-27

• Sample 2026-27 Q1Identify the function from its graph, $\pi + \cos^{-1}x$
  Graphs of inverse trigonometric functions1 mark
• Sample 2026-27 Q2Domain of $\sec^{-1}(2x)$
  Domain of sec⁻¹x1 mark
• Sample 2026-27 Q3Value of $\cot^{-1}\left(2\cos\left(\frac12\sin^{-1}\frac{\sqrt3}{2}\right)\right)$
  Principal values of inverse trig functions1 mark

CBSE Sample Paper 2025-26

• Sample 2025-26 Q1Identify the function from its graph, $\sin^{-1}(2x)$
  Graphs and domains of inverse trig functions1 mark
• Sample 2025-26 Q19$\sin^{-1}\frac{\sqrt3}{2} + \tan^{-1}1 - \sec^{-1}\sqrt2$ and principal branches
  Principal values of inverse trig functions1 mark
• Sample 2025-26 Q21Evaluate $\tan\left(\tan^{-1}(-1) + \frac{\pi}{3}\right)$⁠, or the domain of $\cos^{-1}(3x - 2)$
  Inverse trigonometric functions: value and domain2 marks

CBSE Sample Paper 2024-25

• Sample 2024-25 Q15Identify the graph of $y = \cos^{-1}x$
  Graph of the principal branch of cos⁻¹x1 mark
• Sample 2024-25 Q21Range of $x$ when $\cot^{-1}(3x + 5) > \frac{\pi}{4}$
  Inverse trig: inequality with cot⁻¹2 marks

CBSE Sample Paper 2023-24

• Sample 2023-24 Q21Value of $\sin^{-1}\left(\cos\frac{33\pi}{5}\right)$⁠, or the domain of $\sin^{-1}(x^2 - 4)$
  Inverse trig: principal value; domain2 marks

CBSE Sample Paper 2022-23

• Sample 2022-23 Q19Domain of $\sec^{-1}2x$ and the value of $\sec^{-1}(-2)$
  Domain and range of sec⁻¹x1 mark
• Sample 2022-23 Q21$\sin^{-1}\left[\sin\frac{13\pi}{7}\right]$⁠, or an onto function on $N$ that is not one-one
  Principal value of sin⁻¹; onto, one-one functions2 marks

CBSE Sample Paper 2020-21

• Sample 2020-21 Q19Simplest form of $\tan^{-1}\left(\frac{\cos x}{1 - \sin x}\right)$⁠, $-\frac{3\pi}{2} < x < \frac{\pi}{2}$
  Simplest form of an inverse trigonometric function2 marks

Questions that also use Inverse Trigonometric Functions

Their main topic is in another chapter.

• Board 2023 Q21The set B for a one-one onto $f(x) = 2x$⁠, or $\sin^{-1}\left(\sin\frac{3\pi}{4}\right) + \cos^{-1}\left(\cos\frac{3\pi}{4}\right) + \tan^{-1}1$
  One-one onto function; inverse trig values2 marks
• Sample 2026-27 Q7Derivative of $\cos^{-1}(2x^2 - 1)$ with respect to $\cos^{-1}x$
  Derivative of one function with respect to another1 mark
• Sample 2024-25 Q20Is $f(x) = \sec x$ one-one on its domain?
  One-one functions: sec x and the line test1 mark
• Sample 2022-23 Q24Prove $\frac{dy}{dx} = -\sqrt{\frac{1 - y^2}{1 - x^2}}$ if $y\sqrt{1 - x^2} + x\sqrt{1 - y^2} = 1$
  Derivative using an inverse trig substitution2 marks