NCERT Exemplar Class 12 Maths Chapter 2 - Inverse Trigonometric Functions - Free PDF Download
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What is the NCERT Exemplar Class 12 Maths Chapter 2?
NCERT Exemplar Class 12 Maths Chapter 2 focuses entirely on Inverse Trigonometric Functions, one of the most formula-intensive chapters in the Class 12 syllabus. Published by the National Council of Educational Research and Training (NCERT), the Exemplar book is designed to provide Higher Order Thinking Skills (HOTS) questions that go beyond the standard NCERT textbook.
Why Is the Exemplar Book Different from the NCERT Textbook?
The standard NCERT textbook introduces concepts and provides straightforward exercises. The Exemplar book goes a step further by including multiple-choice questions, short-answer questions, and long-answer problems that test conceptual understanding and analytical thinking. For students aiming to score above 95 marks in Class 12 Mathematics, solving Exemplar questions is highly recommended.
Who Should Use This Chapter's Exemplar Problems?
- Class 12 CBSE students preparing for board examinations
- JEE Main aspirants looking to strengthen inverse trigonometric concepts and identities
- Students who have already completed NCERT textbook exercises and want advanced-level practice
Key Topics Covered in Chapter 2 – Inverse Trigonometric Functions
Chapter 2 builds directly on the trigonometry concepts studied in Class 11. The Exemplar problems cover all major topics from the chapter in greater depth.
Principal Value Branch
Every inverse trigonometric function is defined over a restricted domain to make it one-to-one and onto. Understanding the principal value branch is essential for solving almost every question in this chapter.
| Function | Domain | Range (Principal Value Branch) |
|---|---|---|
| $\sin^{-1}(x)$ | $[-1,1]$ | $[-\pi/2,\pi/2]$ |
| $\cos^{-1}(x)$ | $[-1,1]$ | $[0,\pi]$ |
| $\tan^{-1}(x)$ | $\mathbb{R}$ | $(-\pi/2,\pi/2)$ |
| $\cot^{-1}(x)$ | $\mathbb{R}$ | $(0,\pi)$ |
| $\sec^{-1}(x)$ | $\mathbb{R} - (-1,1)$ | $[0,\pi]-\{\pi/2\}$ |
| $\csc^{-1}(x)$ | $\mathbb{R} - (-1,1)$ | $[-\pi/2,\pi/2]-\{0\}$ |
Properties and Identities of Inverse Trigonometric Functions
This is one of the highest-weightage sections of the chapter. Students should thoroughly memorise and understand the following identities:
- $\sin^{-1}(x)+\cos^{-1}(x)=\frac{\pi}{2}$
- $\tan^{-1}(x)+\cot^{-1}(x)=\frac{\pi}{2}$
- $\sec^{-1}(x)+\csc^{-1}(x)=\frac{\pi}{2}$
- Addition and subtraction formulas involving inverse tangent functions
- Double-angle and expression simplification identities
Conversion Between Inverse Trigonometric Functions
Questions frequently require expressing one inverse trigonometric function in terms of another. Students should practise converting between $\sin^{-1}(x)$, $\cos^{-1}(x)$, $\tan^{-1}(x)$ and $\sec^{-1}(x)$ to improve speed and accuracy in examinations.
The most common mistake students make in this chapter is applying inverse trigonometric identities without checking the domain of the given value. Always verify that the input lies within the valid domain before applying any identity.
What Types of Questions Appear in the NCERT Exemplar Chapter 2?
The NCERT Exemplar Chapter 2 is divided into multiple categories of questions. Understanding the distribution helps students prioritise their preparation effectively.
| Question Type | Approximate Number of Questions | Difficulty Level | Board Relevance | JEE Main Relevance |
|---|---|---|---|---|
| Multiple Choice Questions (MCQs) | 20 | Medium | High | Very High |
| Fill in the Blanks | 10 | Medium | High | Medium |
| True/False Questions | 5 | Low–Medium | Medium | Low |
| Short and Long Answer Questions | 15 | High | Very High | High |
Which Questions Are Most Important for CBSE Boards?
Short-answer and long-answer questions are particularly important because they closely resemble the 3-mark and 5-mark questions asked in CBSE board examinations. Problems involving simplification using inverse trigonometric identities and principal value evaluation are especially important.
Which Questions Are Most Important for JEE Main?
MCQs based on domain-range analysis, principal value concepts, and identity-based simplifications are highly relevant for JEE Main. Inverse Trigonometric Functions consistently appear in the Mathematics section and remain an important scoring topic for competitive examinations.
Download the PDF of NCERT Exemplars Class 12 Maths Chapter 2 “Inverse Trigonometric Functions”
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Frequently Asked Questions
Find answers to common questions.
How many questions are in NCERT Exemplar Class 12 Maths Chapter 2?
NCERT Exemplar Chapter 2 contains approximately 50 questions across four types: Multiple Choice Questions (~20), Fill in the Blanks (~10), True/False (~5), and Short & Long Answer questions (~15). The distribution is designed to test both quick recall and deep conceptual understanding.
Is NCERT Exemplar Class 12 Maths Chapter 2 important for CBSE boards?
Yes, it is directly important. CBSE board papers regularly include 3-mark and 5-mark questions based on inverse trig identities and simplifications — the exact type of problems drilled in the Exemplar. Solving Exemplar Chapter 2 ensures you are practising at a level above what the board paper demands, which directly translates to full marks in this section
What is NCERT Exemplar Class 12 Maths Chapter 2 about?
NCERT Exemplar Class 12 Maths Chapter 2 covers Inverse Trigonometric Functions. It includes problems on principal value branches, domain and range of all six inverse trig functions, and key identities. The Exemplar book provides harder problems than the standard NCERT textbook, making it essential for students targeting 90+ marks in CBSE boards or preparing for JEE Main.
What is the difference between NCERT textbook and NCERT Exemplar for Class 12 Maths Chapter 2?
The NCERT textbook introduces concepts and provides standard exercises at a foundational level. The NCERT Exemplar contains advanced problems — including MCQs, assertion-reasoning, and multi-step application questions — that test higher-order thinking. For scoring 90+ in boards or cracking JEE Main, both books must be completed, in that order.
Where can I download the NCERT Exemplar Class 12 Maths Chapter 2 PDF for free?
You can download it directly from this page using the download link provided in Section 6 above. The PDF is free, contains all questions, and includes step-by-step solutions prepared by eSaral's IIT Bombay faculty. No sign-up is required to access the download.
Is Chapter 2 Inverse Trigonometric Functions important for JEE Main?
Yes. While the chapter has moderate direct weightage in JEE Main, its concepts form the foundation for differentiating and integrating inverse trig expressions in later chapters. JEE Main consistently includes MCQs on domain-range analysis and identity simplification. Weakness in this chapter compounds in Chapters 5 and 7 during JEE preparation.