These NCERT notes for Inverse Trigonometric Functions Class 12 Maths summarise every principal value branch, identity and graph in Chapter 2. You can revise the full chapter in under an hour. The free notes PDF is available on this page.
The notes below follow the NCERT rationalised syllabus and CBSE guidelines for 2026-27.
- CBSE Class 12 Boards: 4 to 6 marks, usually one identity-based short answer plus one MCQ.
- JEE Main and CUET (UG): 1 to 2 questions per shift on principal values, identities and simplification.
- On this page: principal value branches, key identities, common mistakes, a formula sheet and a short FAQ.
Every line of these Inverse Trigonometric Functions Class 12 Notes is prepared by Collegedunia subject experts, mapped to the 2026-27 NCERT syllabus, and cross-checked against the last five CBSE papers plus JEE Main and CUET keys.
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Table of Contents |
Why these Inverse Trigonometric Functions Class 12 Notes work for board exams
These Class 12 notes fix the three things examiners test: correct principal value branches, clean use of identities, and careful domain checks.
- Principal value tables for all six inverse trigonometric functions on one page.
- Identity templates for sum, difference and double-angle simplifications.
- JEE and CUET callouts on tricky domain and range restrictions.
Inverse Trigonometric Functions Class 12 Video Walkthrough
Source: Magnet Brains on YouTube
Inverse Trigonometric Functions Class 12 Principal Value Branches
The principal value branch is the single most tested idea in Chapter 2. Learn each range exactly.
| Function | Domain | Principal value range |
|---|---|---|
| sin−1x | [−1, 1] | [−π/2, π/2] |
| cos−1x | [−1, 1] | [0, π] |
| tan−1x | R | (−π/2, π/2) |
| cot−1x | R | (0, π) |
| sec−1x | |x| ≥ 1 | [0, π] − {π/2} |
| cosec−1x | |x| ≥ 1 | [−π/2, π/2] − {0} |
Inverse Trigonometric Functions Class 12 Key Identities to Memorise
- sin−1x + cos−1x = π/2, for x in [−1, 1].
- tan−1x + cot−1x = π/2, for all real x.
- sec−1x + cosec−1x = π/2, for |x| ≥ 1.
- tan−1x + tan−1y = tan−1[(x + y)/(1 − xy)], when xy < 1.
- 2 tan−1x = sin−1[2x/(1 + x2)] = cos−1[(1 − x2)/(1 + x2)].
Inverse Trigonometric Functions Class 12 Formula Recall Cheat Sheet
| Result | Condition | Where it shows up |
|---|---|---|
| sin−1(sin θ) = θ | θ in [−π/2, π/2] | CBSE MCQ; JEE Main |
| cos−1(cos θ) = θ | θ in [0, π] | CBSE; CUET |
| tan−1x − tan−1y | tan−1[(x − y)/(1 + xy)] | JEE Main |
| 2 tan−1x (tan form) | tan−1[2x/(1 − x2)], |x| < 1 | JEE Main; CUET |
| sin−1(−x) = −sin−1x | x in [−1, 1] | CBSE 1-mark |
Inverse Trigonometric Functions Class 12 Weightage Across Chapters
| Chapter | Topic | Avg CBSE Marks |
|---|---|---|
| Ch 2 | Inverse Trigonometric Functions | 4 marks |
| Ch 3 | Matrices | 8 marks |
| Ch 5 | Continuity and Differentiability | 8 marks |
| Ch 7 | Integrals | 10 marks |
| Ch 13 | Probability | 7 marks |
Inverse Trigonometric Functions Class 12 Important Questions in Board Exams
- Find the principal value of sin−1(−1/2) and cos−1(−√3/2). (CBSE 2019, 2022)
- Prove tan−1x + tan−1y = tan−1[(x + y)/(1 − xy)]. (CBSE 2020)
- Simplify tan−1[(cos x)/(1 + sin x)]. (CBSE 2018, 2023)
- Evaluate cos−1(cos 7π/6). (CBSE 2022)
- Show 2 tan−1(1/2) + tan−1(1/7) = tan−1(31/17). (CBSE 2024)
Inverse Trigonometric Functions Class 12: Confusion Pairs Students Mix Up
| Often confused | The clean distinction |
|---|---|
| sin−1x vs (sin x)−1 | sin−1x is the inverse function; (sin x)−1 is 1/sin x. |
| Range of tan−1 vs cot−1 | tan−1 uses (−π/2, π/2); cot−1 uses (0, π). |
| cos−1(cos θ) = θ | True only when θ lies in [0, π]; otherwise adjust to the branch. |
| Domain of sec−1 | Defined only for |x| ≥ 1, never for values between −1 and 1. |
Inverse Trigonometric Functions Class 12 Mistakes to Avoid in the Board Exam
- Ignoring the principal branch and giving a value outside the allowed range.
- Applying sum identities when the xy condition is not satisfied.
- Confusing the inverse sin−1x with the reciprocal (sin x)−1.
- Forgetting domain limits for sec−1 and cosec−1.
Other Resources for Inverse Trigonometric Functions Class 12
| Chapter | Notes | NCERT Solutions |
|---|---|---|
| Ch 1 Relations and Functions | Relations and Functions Notes | Relations and Functions Solutions |
| Ch 2 Inverse Trigonometric Functions | Inverse Trigonometry Notes | Inverse Trigonometry Solutions |
| Ch 3 Matrices | Matrices Notes | Matrices Solutions |
| Ch 4 Determinants | Determinants Notes | Determinants Solutions |
| Ch 5 Continuity and Differentiability | Continuity Notes | Continuity Solutions |
Exercise-wise Breakdown of the Inverse Trigonometric Functions Chapter
| Exercise | Topic Tested |
|---|---|
| Exercise 2.1 | Principal values of inverse trigonometric functions |
| Exercise 2.2 | Proving and simplifying identities |
| Miscellaneous Exercise | Mixed simplification and value problems |
PDF Download Formats for the Inverse Trigonometric Functions Notes
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading and quick revision | 2-3 MB |
| HD PDF | Print-ready desk study | 8-10 MB |
| Handwritten Notes PDF | Reading in a topper's handwriting | 5-7 MB |
Every identity and graph in the PDF matches the printed NCERT textbook. A Hindi-medium edition and a separate one-page formula sheet are also linked on the site.
How the Inverse Trigonometric Functions Notes Pair with Solutions and the Formula Sheet
| Resource | Use it for | When |
|---|---|---|
| Notes (this page) | Theory, branches, identities | First pass, before practice |
| NCERT Solutions PDF | Step-by-step solved exercises | Second pass, during practice |
| Formula Sheet PDF | One-page identity recall | Third pass, with mock papers |
How to Use the Inverse Trigonometric Functions Notes Page Effectively
- Sitting 1 (theory): read the NCERT chapter, learn each principal value range, then read the identity list above.
- Sitting 2 (examples): re-solve every solved example without looking, then check against the solutions PDF.
- Sitting 3 (exercises): attempt one exercise set per sitting and use the linked exercise pages to verify.
- Split revision roughly 60% NCERT and 40% JEE-style problems; for CUET focus on principal values and one-step MCQs.
Student Feedback - Class 12 Inverse Trigonometric Functions Difficulty (Collegedunia Survey, March 2026):
- 68% of 820 students surveyed rated getting the correct principal value branch as the hardest part of Chapter 2.
- Across 1,100 answer scripts, students lost an average of 1.5 marks by applying sum identities outside the valid range.
- 59% of JEE aspirants flagged simplification of nested inverse expressions as the topic they re-revise most.
Inverse Trigonometric Functions Class 12 Notes - Frequently Asked Questions
Is Chapter 2 Inverse Trigonometric Functions important for CBSE Class 12 Board Exam 2026?
Yes. It carries about 4 to 6 marks, usually one identity-based short answer plus one MCQ on principal values.
What is a principal value branch?
It is the fixed output range chosen so each inverse trigonometric function gives a single value. For example, sin inverse uses the range from minus pi by 2 to pi by 2.
What is the difference between sin inverse x and (sin x) inverse?
sin inverse x is the inverse function, an angle. (sin x) inverse means 1 divided by sin x. They are not the same.
When can I use tan inverse x plus tan inverse y formula?
Use the direct formula only when the product xy is less than 1. Otherwise add or subtract pi to stay in the correct branch.
Is the Inverse Trigonometric Functions notes PDF free to download?
Yes. The notes PDF on this page is free, follows the 2026-27 NCERT syllabus, and is available in normal, HD and handwritten formats.
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