Last Updated on July 29, 2025 by XAM CONTENT
To succeed in Class 12 Maths exams, a strong grasp of Chapter 2 – Inverse Trigonometric Functions is essential. Our comprehensive collection of chapterwise MCQ questions with answers for Class 12 Maths is designed according to the latest syllabus and exam guidelines, ensuring targeted preparation and better performance. It is a part of MCQ Questions for CBSE Class 12 Maths Series.
These multiple-choice questions will help you assess your knowledge, improve accuracy, and boost confidence for your exams. Whether you are preparing for school tests, online tests or competitive exams, these Inverse Trigonometric Functions MCQs will strengthen your conceptual clarity.
| Chapter | Inverse Trigonometric Functions |
| Book | Maths for Class 12 |
| Type of Questions | MCQ Questions |
| Nature of Questions | Competency Based Questions |
| Board | CBSE |
| Class | 12 |
| Subject | Maths |
| Useful for | Class 12 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| Important Link | Class 12 Maths Chapterwise MCQ Questions |
MCQ Questions on Inverse Trigonometric Functions Class 12 Maths (PDF Download)
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Answer: (a) $\frac{\pi}{2}$Explanation: Principal value of $\sin^{-1}(1)$ is $\frac{\pi}{2}$, as $\sin\frac{\pi}{2}=1$ and the range of $\sin^{-1}x$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$.
2. The value of $\cos^{-1}(-1/2)$ is
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Answer: (c) $\frac{2\pi}{3}$Explanation: $\cos(\frac{2\pi}{3}) = -\frac{1}{2}$ and $\cos^{-1}x$ has principal value in $[0, \pi]$.
3. Evaluate $\tan^{-1}(\sqrt{3}) + \sec^{-1}(2) – \cos^{-1}(1)$.
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Answer: (b) $\frac{2\pi}{3}$Explanation: $\tan^{-1}(\sqrt{3}) = \frac{\pi}{3}$, $\sec^{-1}(2)=\frac{\pi}{3}$, $\cos^{-1}(1)=0$. Sum = $\frac{\pi}{3} + \frac{\pi}{3} – 0 = \frac{2\pi}{3}$.
4. The principal value of $\tan^{-1}(-\sqrt{3})$ is
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Answer: (a) $-\frac{\pi}{3}$Explanation: $\tan(-\frac{\pi}{3}) = -\sqrt{3}$ and range of $\tan^{-1}x$ is $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$.
5. The value of $\sin^{-1} \left( \frac{1}{2} \right) + \cos^{-1} \left( \frac{1}{2} \right)$ is
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Answer: (b) $\frac{\pi}{2}$Explanation: For any $x\in[-1,1]$, $\sin^{-1}x+\cos^{-1}x = \frac{\pi}{2}$.
6. The principal value of $\sec^{-1}(-2)$ is
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Answer: (c) $2\pi/3$Explanation: $\sec(2\pi/3) = -2$; principal value of $\sec^{-1}x$ for $x<0$ is in $[\pi/2, \pi]$.
7. The value of $\sin^{-1}(x) + \sin^{-1}(\sqrt{1-x^2})$ (for $x\in[-1,1]$) is
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Answer: (b) $\frac{\pi}{2}$Explanation: If $y = \sin^{-1} x$, then $z = \sin^{-1}(\sqrt{1-x^2}) = \frac{\pi}{2}-y$, so their sum is $\frac{\pi}{2}$.
8. If $y = \sin^{-1}(\sin x)$, then
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Answer: (b) $y = x$ for $x\in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$Explanation: By definition, $\sin^{-1}(\sin x) = x$ where $x$ is in the principal branch $[-\frac{\pi}{2},\frac{\pi}{2}]$.
9. The value of $\tan^{-1}1 + \tan^{-1}2 + \tan^{-1}3$ is
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Answer: (b) $\pi$Explanation: $\tan^{-1}1=\frac{\pi}{4}$, $\tan^{-1}2+\tan^{-1}3=\frac{\pi}{4}+\frac{\pi}{2}=\frac{3\pi}{4}$, sum is $\pi$.
10. If $\tan^{-1}x + \tan^{-1}y = \frac{\pi}{4}$, then $x+y = $
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Answer: (a) $1$Explanation: $\tan^{-1}x+\tan^{-1}y=\tan^{-1}\left(\frac{x+y}{1-xy}\right)$, so if sum $=\frac{\pi}{4}$, $\tan(\frac{\pi}{4})=1$, so $\frac{x+y}{1-xy}=1 \implies x+y = 1-xy \implies x+y+xy=1$.
11. What is the principal value of $\cot^{-1}(\cot 3\pi/4)$?
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Answer: (a) $\frac{3\pi}{4}$Explanation: For $y = \cot^{-1}(\cot x)$, $y\in(0,\pi)$, so $\cot^{-1}(\cot 3\pi/4) = 3\pi/4$ (since it already falls in the principal branch).
12. If $f(x) = \textrm{tan}^{-1} x$, then $f^{-1}(x) =$
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Answer: (b) $\tan x$Explanation: If $f(x)=\tan^{-1}x$, $f^{-1}(x)=\tan x$ on the domain of principal values.
13. The domain of the function $f(x) = \sin^{-1}(2x)$ is
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Answer: (b) $[-\frac{1}{2},\frac{1}{2}]$Explanation: $-1 \leq 2x \leq 1 \implies x\in\left[-\frac{1}{2},\frac{1}{2}\right]$.
14. If $\sin^{-1}(x) + \sin^{-1}(y) = \frac{\pi}{2}$, then $x^2 + y^2$ equals
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Answer: (c) $1$Explanation: $\sin^{-1}(x) + \sin^{-1}(y) = \frac{\pi}{2} \implies y = \cos^{-1}(x) \implies y=\sqrt{1-x^2}$ within proper sign, so $x^2 + y^2 = x^2 + (1-x^2) = 1$
15. The principal value branch of $\tan^{-1}x$ is
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Answer: (b) $[-\frac{\pi}{2}, \frac{\pi}{2}]$Explanation: The principal value of $\tan^{-1}x$ is $(-\frac{\pi}{2}, \frac{\pi}{2})$.
We hope the given mcq questions with Answers for Inverse Trigonometric Functions Class 12 helps you in your learning.
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Also check
- Inverse Trigonometric Functions – Class 12 Maths Chapter 2 MCQ Questions with Answers (Updated)
- Relations and Functions – Class 12 Maths Chapter 1 MCQ Questions with Answers (Updated)
Topics from which mcq questions may be asked
- Definition and domain
- Principal value branch
- Properties and graphs
Inverse trigonometry bridges geometry and advanced algebra.
Frequently Asked Questions (FAQs) on Inverse Trigonometric Functions MCQ Questions
Q1: What are inverse trigonometric functions and why are they significant?
A1: Inverse trigonometric functions reverse the process of the standard trigonometric functions, allowing you to determine the angle when the trigonometric ratio is given. They are especially important in calculus, coordinate geometry, and solving real-world engineering and physics problems.
Q2: What is meant by the principal value of an inverse trigonometric function?
A2: The principal value of an inverse trigonometric function is the unique value an inverse takes within its principal branch – a specific range where the function is defined as one-to-one. Mentioning the principal value is crucial for scoring full marks in CBSE exams.
Q3: What are the domain and range restrictions for inverse trigonometric functions?
A3: Each inverse trigonometric function has specific domain and range restrictions needed to ensure they act as true functions.
Q4: What are the most common types of questions asked from this chapter in board exams and competitive tests?
A4: Questions typically include evaluating principal values, applying domain and range restrictions, using properties and identities of inverse trigonometric functions, and solving MCQs involving simplification of expressions or formulae conversions.
Q5: Why is practising MCQs important for Chapter 2 of Class 12 Maths, and what are the best resources?
A5: Practising MCQs builds conceptual clarity, improves speed and accuracy, and prepares students for the format of the CBSE exam, which increasingly emphasizes objective-type questions. Recommended resources include chapter-wise MCQ compilations and explanations from leading educational platforms such as Physics Gurukul, EbookPublisher, and Xam Content.
