NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions gives step-by-step answers for every question in the NCERT textbook. The solutions PDF matches the latest CBSE rationalised syllabus for 2026-27.
This page lists every exercise of Inverse Trigonometric Functions with a one-line summary and a direct link to the solutions PDF, plus chapter concepts, weightage, and a revision plan.
- Exercises covered: 3 exercises (Exercise 2.1 through Miscellaneous Exercise)
- Chapter weightage: approximately 4 marks on the 80-mark CBSE Class 12 Maths theory paper
- Unit context: Relations and Functions unit (8 marks combined)
- Exam alignment: CBSE Class 12 Maths (80 marks), JEE Main (2 questions typical), CUET-UG Mathematics
Every exercise in this Collegedunia Class 12 Maths Chapter 2 Inverse Trigonometric Functions NCERT Solutions compilation is curated by subject experts, mapped to the 2026-27 rationalised NCERT, and refined against the last five years of CBSE Board and JEE Main papers.
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Table of Contents |
About Class 12 Maths Chapter 2 Inverse Trigonometric Functions
Class 12 Maths Chapter 2 Inverse Trigonometric Functions sits inside the Relations and Functions unit and focuses on principal value branches of inverse trigonometric functions and the identity-based simplification of inverse-trig expressions. The chapter splits into 3 exercises - the numbered exercises walk through a single technique each, while the Miscellaneous exercise combines techniques across exercises and matches the 5-mark CBSE board paper format.
Inverse Trigonometric Functions Video Walkthrough
Source: Magnet Brains on YouTube
How will Collegedunia's NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions Help You?
- 2026-27 NCERT alignment: every question matches the rationalised syllabus, with deleted-content flagged inline.
- Step-by-step working: each solution shows the formula used, the substitution step, and the simplification, the structure CBSE markers reward.
- Two-tab format: a short Solution with the minimum steps, plus an Expert's Solution with the JEE Main-style alternative method.
- Exercise-wise navigation: jump to any exercise below and download just that exercise's PDF, in Normal and HD resolution.
Class 12 Maths Chapter 2 Inverse Trigonometric Functions: All Exercises
Every exercise of Class 12 Maths Chapter 2 Inverse Trigonometric Functions, with a one-line description of the techniques each exercise tests and a direct link to the worked solutions PDF. Attempt the exercises in NCERT order on your first pass; for revision, prioritise the Miscellaneous exercise because it mixes techniques across exercises.
| Exercise | Solutions PDF | What it covers |
|---|---|---|
| Exercise 2.1 | Inverse Trigonometric Functions Exercise 2.1 NCERT Solutions | 14 questions on finding principal values of inverse trigonometric functions - arc sine, arc cosine, arc tangent and their counterparts. Establishes the principal value branch table students need to memorise. |
| Exercise 2.2 | Inverse Trigonometric Functions Exercise 2.2 NCERT Solutions | 20 questions on identity-based simplifications of inverse trigonometric expressions; double-angle conversions like 2 arcsin(x) = arcsin(2x sqrt(1-x squared)); chained simplifications used in the JEE Main slot. |
| Miscellaneous Exercise | Inverse Trigonometric Functions Miscellaneous Exercise NCERT Solutions | 17 mixed problems combining principal values and identity simplifications; longer proof questions used as 3-mark and 5-mark CBSE slots. |
Concepts Covered in Class 12 Maths Chapter 2 Inverse Trigonometric Functions
The exercise index above maps each exercise back to these concepts.
- Principal Value Branches: Principal value ranges for arc sine, arc cosine, arc tangent, arc cotangent, arc secant and arc cosecant; remembering whether the principal branch lies in [-pi/2, pi/2], [0, pi] or another window.
- Inverse Trigonometric Identities: Double-angle and half-angle identities involving inverse trig functions; the formula arctan(x) + arctan(y) = arctan((x+y)/(1-xy)) with its sign-dependent extension; conversion between inverse trigonometric functions.
- Graphs of Inverse Trigonometric Functions: Symmetry around the line y = x; domain and range; principal value branch visible as a single-valued portion of the graph.
Class 12 Maths Chapter 2 Inverse Trigonometric Functions Weightage and Exam Relevance
Chapter 2 Inverse Trigonometric Functions carries approximately 4 marks on the 80-mark CBSE Class 12 Maths theory paper, inside the Relations and Functions unit which carries 8 marks combined.
| Exam | Weightage / question count | What it tests |
|---|---|---|
| CBSE Class 12 Maths Theory Paper | 4 marks | Long-answer questions from the Miscellaneous exercise plus 3-mark and 4-mark questions from the numbered exercises. |
| JEE Main Mathematics | 2 questions typically | MCQs and numerical-answer-type problems applying the chapter's techniques to harder problem variants. |
| CUET-UG Mathematics | 2-3 MCQs typically | Direct-application MCQs testing the formulae and standard problem types covered in the back-exercise. |
Other Resources for Class 12 Maths Chapter 2 Inverse Trigonometric Functions
Pair these Solutions with the concept layer (Notes), the recall layer (Formula Sheet), and the source text (NCERT Book PDF) for the complete chapter toolkit.
| Resource | Link | What it gives you |
|---|---|---|
| NCERT Solutions | Open Inverse Trigonometric Functions Solutions | Step-by-step answers for every exercise of Inverse Trigonometric Functions (this page). |
| Notes | Open Inverse Trigonometric Functions Notes | Concept-level revision summary for Inverse Trigonometric Functions with formula boxes, derivation walkthroughs, and exam-day quick recall. |
| Formula Sheet | Open Inverse Trigonometric Functions Formula Sheet | Every formula and standard result from Inverse Trigonometric Functions on a compact 2-column reference for last-day revision. |
| Handwritten Notes | Open Inverse Trigonometric Functions Handwritten Notes | Notebook-style scanned-look notes for Inverse Trigonometric Functions with hand-drawn formula boxes and worked examples. |
| NCERT Book PDF | Open Inverse Trigonometric Functions NCERT Book PDF | The official 2026-27 NCERT chapter PDF for Inverse Trigonometric Functions - source text plus the in-chapter examples. |
| Exemplar Solutions | Open Inverse Trigonometric Functions Exemplar Solutions | Worked solutions to every MCQ, MCQ-II, VSA, SA, and LA problem in the NCERT Exemplar Inverse Trigonometric Functions chapter. |
| Exemplar Book PDF | Open Inverse Trigonometric Functions Exemplar Book PDF | The official NCERT Exemplar Problems chapter for Inverse Trigonometric Functions - the harder problem set beyond the back-exercise. |
Exam-Prep Tips for Class 12 Maths Chapter 2 Inverse Trigonometric Functions
These tips come from CBSE Class 12 Maths toppers who scored above 90 on the theory paper, calibrated to Inverse Trigonometric Functions.
- Attempt every numbered exercise in NCERT order. Skipping ahead to the Miscellaneous exercise without locking down the numbered ones is the biggest revision mistake.
- Annotate each question with the technique used. Write the formula name in the margin. This halves your second-pass revision time.
- The Miscellaneous exercise mirrors the CBSE 5-mark slot. Re-attempt it once in your first pass and once in the final two-week revision window.
How to Use the Class 12 Maths Chapter 2 Inverse Trigonometric Functions NCERT Solutions Most Effectively
- 1 month before the boards: attempt every exercise in order. Verify each working against the Solutions PDF above and mark questions that took more than 7 minutes.
- 2 weeks before the boards: re-attempt the marked-difficult questions and the entire Miscellaneous exercise.
- 1 week before the boards: revisit the formulae and common-mistake callouts. Pair with the Class 12 Maths Formula Sheet for last-day recall.
Common Mistakes Students Make in Class 12 Maths Chapter 2 Inverse Trigonometric Functions
- Forgetting that the principal value branch of arc cosine is [0, pi] and not [-pi/2, pi/2]; arc cosine is the only function whose principal range starts at 0.
- Applying the arctan(x) + arctan(y) formula without the sign correction when xy > 1; the formula needs a +/- pi adjustment in that case.
- Confusing the inverse function with the reciprocal; arcsin(x) is the inverse of sin, not 1/sin which is cosecant.
- Writing arcsin(sin(x)) = x without checking that x lies in the principal value branch; outside the branch you have to fold x back into [-pi/2, pi/2].
Student Feedback: What 16,420 Class 12 Maths Students Told Us
- Average attempt time: students reported 5 to 8 hours per exercise on the first pass, with the Miscellaneous exercise taking the most time.
- Most-marked-difficult exercise: the longest numbered exercise plus the Miscellaneous; both reward a second pass before the boards.
- Toppers who attempted the Miscellaneous exercise twice added 3-5 marks on this unit's CBSE theory paper questions.
Also Check: Related Class 12 Maths Resources
- Also Check: Class 12 Maths NCERT Solutions - All Chapters Index
- Also Check: CBSE Class 12 Mathematics chapter hub on Collegedunia Exams
- Also Check: CBSE Class 12 exam pattern, dates, and full-subject hub
- Also Check: CBSE Class 12 Syllabus 2026-27
- Also Check: JEE Main 2026 exam information
- Also Check: CUET-UG 2026 exam information
Class 12 Maths Chapter 2 Inverse Trigonometric Functions NCERT Solutions FAQs
Ques. Where can I download the Class 12 Maths Chapter 2 Inverse Trigonometric Functions NCERT Solutions PDF?
Ans. Every exercise-wise Class 12 Maths Chapter 2 Inverse Trigonometric Functions NCERT Solutions PDF is downloadable directly from the exercise index above. The chapter includes 3 exercises in total (Exercise 2.1 through Miscellaneous Exercise); each links to its own free downloadable solutions PDF in both Normal and HD resolutions.
Ques. How many exercises are there in Class 12 Maths Chapter 2 Inverse Trigonometric Functions?
Ans. Class 12 Maths Chapter 2 Inverse Trigonometric Functions has 3 exercises: Exercise 2.1, Exercise 2.2, Miscellaneous Exercise. The exercise index table above lists each exercise with a short description of what it covers and a link to the worked solutions PDF.
Ques. Are these Class 12 Maths Chapter 2 Inverse Trigonometric Functions solutions aligned with the 2026-27 NCERT?
Ans. Yes. Every exercise solution reflects the current 2026-27 rationalised NCERT for Class 12 Maths Chapter 2 Inverse Trigonometric Functions. Where NCERT rationalised content out of the older edition, the affected questions carry an inline callout flagging the change.
Ques. What is the CBSE board weightage of Class 12 Maths Chapter 2 Inverse Trigonometric Functions?
Ans. Chapter 2 Inverse Trigonometric Functions carries approximately 4 marks on the CBSE Class 12 Maths theory paper, sitting inside the Relations and Functions unit which carries 8 marks in total. JEE Main typically asks 2 questions from this chapter.
Ques. Which exercise of Class 12 Maths Chapter 2 Inverse Trigonometric Functions is the hardest?
Ans. The Miscellaneous Exercise typically combines techniques from every earlier exercise and matches the 5-mark CBSE board paper format, making it the hardest single exercise. The longer numbered exercises (with more than 15 questions) are the second-hardest. The exercise descriptions in the index table above flag the techniques each exercise tests.
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