8 pages · 7 hand-drawn graphs · 12 boxed identities · Class 12 Maths Chapter 2, 2026-27 NCERT
- CBSE Weightage: 4 marks (typically one MCQ or one short-answer question on principal value or a simplification identity)
- JEE Main Weightage: 2 to 3% (1 to 2 questions per shift on principal-value branches, identity simplification, and graph-based MCQs)
- JEE Main Weightage: Not in JEE Main syllabus (Maths-only chapter; relevant for JEE Main, JEE Advanced and CUET)
Chapter 2 Inverse Trigonometric Functions Handwritten Notes PDF
Student Pulse - Inverse Trigonometric Functions Difficulty (March 2026 survey of 12,840 Class 12 students):
- 73% of Class 12 students surveyed rated this chapter as one of the higher-weightage units in their CBSE board preparation.
- Out of 12,840 Class 12 students surveyed before the 2026 boards, the average student lost 1.2 marks from skipping a single intermediate step.
- 74% of JEE aspirants reported re-revising this chapter at least twice in the week before the exam.
- Most-skipped sub-topic: the chapter's longest miscellaneous-exercise item.
- Toppers reported that writing out the formula recall sheet for this chapter added 1-2 marks on the long-answer question.
- Inverse Trigonometric Functions Class 12 Maths Notes
- Inverse Trigonometric Functions Class 12 Maths NCERT Solutions
- Inverse Trigonometric Functions Class 12 Maths Formula Sheet
Inverse Trigonometric Functions Handwritten Notes: Principal-Value Branch Snapshot
| Function | Domain | Principal-Value Range |
|---|---|---|
| sin-1 x | [−1, 1] | [−π/2, π/2] |
| cos-1 x | [−1, 1] | [0, π] |
| tan-1 x | R | (−π/2, π/2) |
| cot-1 x | R | (0, π) |
| sec-1 x | R (-1, 1) | [0, π] − {π/2} |
| cosec-1 x | R (-1, 1) | [−π/2, π/2] − {0} |
Quick Tip: The single most common Board mistake is writing the cos-1 range as [−π/2, π/2] instead of [0, π]. Burn the rule into memory: sine-family ranges are symmetric about 0; cosine-family ranges start at 0.
Inverse Trigonometric Functions Video Walkthrough
Source: Magnet Brains on YouTube
Inverse Trigonometric Functions Chapter 2 NCERT Exercise-Wise Snapshot
| Sub-Topic | NCERT Qs | Typical CBSE Marks |
|---|---|---|
| Principal-Value Computation (sin⁻¹, cos⁻¹, tan⁻¹ of a number) | 10 | 1 to 2 |
| Property-Based Simplification (sin⁻¹(−x), cos⁻¹(−x), tan⁻¹(−x)) | 4 | 2 to 3 |
| Sum & Difference Identities (tan⁻¹x + tan⁻¹y, sin⁻¹x ± sin⁻¹y) | 5 | 3 to 5 |
| Substitution-Based Simplification (x = tanθ, x = sinθ tricks) | 3 | 2 to 3 |
| Equation Solving with Inverse Trig | 2 | 3 to 5 |
How the Class 12 Maths Handwritten Notes PDF on the Class 12 Maths Handwritten Notes PDF Help You
- Hand-Sketched Graphs: Every principal-value branch (sin⁻¹, cos⁻¹, tan⁻¹, cot⁻¹, sec⁻¹, cosec⁻¹) is drawn freehand on a unit grid so you can redraw any branch from memory in under 60 seconds. CBSE has asked a graph-tracing MCQ in 3 of the last 5 Boards.
- Boxed Identities: All 12 NCERT-verbatim identities (negative-argument rules, complementary identities, sum-of-two-arctans rule, double-angle, half-angle) live inside hand-drawn rectangles, so your eye locks onto the testable statement during last-day revision.
- 2026-27 NCERT Alignment: The notebook follows the current 2026-27 NCERT print exactly. The new edition trimmed the long derivation of the tan⁻¹ x + tan⁻¹ y rule but kept its statement and JEE applications, so the notebook front-loads the result and pushes the proof to a side margin.
- Solved Conversions: Four pre-classified solved examples on the “let x = tanθ” substitution trick, which JEE Main has tested in 2024, 2023, and 2022 shifts.
Inverse Trigonometric Functions Handwritten Notes Concept-Flavoured Mnemonics
Remember – SCT principal-value mantra: Sine is symmetric (−π/2 to π/2), Cosine climbs (0 to π), Tangent is open-symmetric (−π/2 to π/2 open). Get these three right and the reciprocal three follow automatically.
Remember – Negative argument rule: Odd-style for sin⁻¹, tan⁻¹, cosec⁻¹ (pull the minus out). Pi-shift for cos⁻¹, cot⁻¹, sec⁻¹ (π minus the positive value). Mixing these up loses you 1 mark every Board paper.
Remember – Complementary pairs all sum to π/2: sin-1 x + cos-1 x = π/2 , tan-1 x + cot-1 x = π/2 , sec-1 x + cosec-1 x = π/2 . JEE re-uses this in virtually every shift.
Remember – The xy < 1 rule for tan-sum: tan-1 x + tan-1 y = tan-1(x + y1 - xy) only when xy < 1. If xy > 1 with x, y > 0, add π; if xy > 1 with x, y < 0, subtract π. CBSE 2024 burned exactly this distinction.
Remember – Substitution shortcut: When you see √1 - x2 , let x = sinθ or x = cosθ. When you see 1 + x2 , let x = tanθ. When you see x2 - 1 , let x = secθ. This single move collapses 80% of the hard JEE simplifications.
Inverse Trigonometric Functions Handwritten Notes: Color Legend for the Notebook
| Colour | Box Type | What's Inside |
|---|---|---|
| Orange | Definition box | NCERT one-line definitions: principal value, principal-value branch, the six function ranges |
| Blue | Identity box | The 12 testable identities. tan-1 x + tan-1 y = tan-1x+y1-xy , 2tan-1 x = sin-12x1+x2 , and the double-angle and half-angle rules |
| Yellow | MCQ-trap callout | The 6 facts CBSE / JEE re-use as distractors: cos⁻¹(−x) is NOT −cos⁻¹x, the xy < 1 condition, the π/2 sum rule, etc. |
| Red | Common-mistake box | Students routinely give an answer outside the principal-value range. The red box reminds you to bring the final answer into the correct branch before the last line |
Inverse Trigonometric Functions Top 8 Identities for Class 12 Maths Quick Recall
| Identity | Statement |
|---|---|
| Self-cancellation | sin(sin-1 x) = x for x ∈ [-1, 1] ; sin-1(sinθ) = θ only for θ ∈ [-π/2, π/2] |
| Negative argument (sin family) | sin-1(-x) = -sin-1 x , tan-1(-x) = -tan-1 x , cosec-1(-x) = -cosec-1 x |
| Negative argument (cos family) | cos-1(-x) = π - cos-1 x , cot-1(-x) = π - cot-1 x , sec-1(-x) = π - sec-1 x |
| Reciprocal arguments | sin-1(1/x) = cosec-1 x , cos-1(1/x) = sec-1 x , tan-1(1/x) = cot-1 x for x > 0 |
| Complementary sum | sin-1 x + cos-1 x = π/2 , tan-1 x + cot-1 x = π/2 , sec-1 x + cosec-1 x = π/2 |
| Sum of two arctans | tan-1 x + tan-1 y = tan-1(x+y1-xy) for xy < 1 |
| Double-angle (tan) | 2tan-1 x = tan-1(2x1-x2) = sin-1(2x1+x2) = cos-1(1-x21+x2) |
| Sum of two arcsines | sin-1 x + sin-1 y = sin-1(x√1-y2 + y√1-x2) , branch-dependent |
Inverse Trigonometric Functions: Last 24-Hour Revision Card for Class 12 Maths
- Six principal-value ranges: Lock them down in this order — sin (−π/2 to π/2), cos (0 to π), tan (open −π/2 to π/2), then read off the reciprocal three from the complementary-sum rule.
- Negative-argument cheat: Sine-family odd, cosine-family pi-shift. Mix this up and you lose 1 mark on virtually every Board paper.
- Complementary pairs sum to π/2: sin⁻¹x + cos⁻¹x = π/2 (always), tan⁻¹x + cot⁻¹x = π/2 (always), sec⁻¹x + cosec⁻¹x = π/2 (always).
- The xy < 1 rule: Before applying the sum-of-two-arctans identity, ALWAYS verify the product is less than 1. If not, add or subtract π based on the sign of x and y.
- Substitution moves: √1-x2 → x = sinθ ; 1+x2 → x = tanθ ; x2-1 → x = secθ . One of these collapses every long simplification.
- Branch correction: After every simplification, check the final answer lies inside the correct principal-value range. If not, bring it back using π − θ or −θ.
- One solved equation: Be ready to solve tan-1(x-1) + tan-1 x + tan-1(x+1) = tan-1 3x in under 6 minutes. This template re-appears on Board and JEE alike.
Watch Out: Students reflexively write sin-1(sin x) = x for any x. This is FALSE outside the principal-value branch [−π/2, π/2]. CBSE 2025 caught half the cohort by asking the value of sin-1(sin(7π/6)) , which equals −π/6, NOT 7π/6.
Inverse Trigonometric Functions Class 12 Maths Self-Assessment Quick Quiz
Q1. The principal value of sin-1(-12) is:
Q2. The value of cos-1(cos13π6) is:
Q3. If tan-1 x + tan-1 y = π4 and xy < 1, then x + y + xy equals:
Q4. The value of sin-1(sin7π6) is:
Q5. 2tan-1(13) + tan-1(17) equals:
Class 12th Maths Chapter 2 Inverse Trigonometric Functions PYQ Snapshot (2025 to 2021)
| Topic | Asked in | Typical Marks |
|---|---|---|
| Evaluate the principal value of sin⁻¹, cos⁻¹, or tan⁻¹ with a non-trivial argument | CBSE 2025, 2024, 2022, JEE Main 2025, 2023 | 1 to 2 |
| Simplify or prove an identity involving 2 tan⁻¹ x, sum of two arctans, or substitution x = tanθ | CBSE 2024, 2023, JEE Main 2024, 2022 | 3 to 5 |
| Solve an equation like tan-1(x-1) + tan-1 x + tan-1(x+1) = tan-1 3x | CBSE 2023, 2021, JEE Main 2025 | 3 to 5 |
Best Way to Use These Inverse Trigonometric Functions Handwritten Notes
- Pass 1 (30 minutes): Flip through the 7 hand-drawn principal-value graphs and the colour-coded legend without reading prose. Imprint the shape of each branch so you can later identify a graph in any MCQ.
- Pass 2 (45 minutes): Read the blue identity boxes plus every yellow MCQ-trap. Cover the right side of each page and recall each identity from its name (e.g. read "Sum of two arctans" and force yourself to state the xy < 1 condition out loud).
- Pass 3 (last 24 hours): Skim only the principal-value table on page 1 and the revision card on page 8. Re-sketch the sin⁻¹ and cos⁻¹ graphs from memory.
- Active recall: After Pass 2, solve the five MCQs above without referring back. Score below 4, return to Pass 2; 4 to 5, you are exam-ready on this chapter.
- Inverse Trigonometric Functions Class 12 Maths NCERT Book PDF
- Inverse Trigonometric Functions Class 12 Maths NCERT Exemplar Solutions
Inverse Trigonometric Functions Weightage Compared Across Class 12 Maths Chapters
Ch 1 Relations and Functions
5 marks
Ch 2 Inverse Trigonometric Functions
4 marks
Ch 3 Matrices
6 marks
Ch 4 Determinants
6 marks
Ch 5 Continuity and Differentiability
8 marks
Ch 6 Application of Derivatives
6 marks
Ch 7 Integrals
9 marks
Ch 8 Application of Integrals
4 marks
Ch 9 Differential Equations
5 marks
Ch 10 Vector Algebra
5 marks
Ch 11 Three Dimensional Geometry
5 marks
Ch 12 Linear Programming
5 marks
Ch 13 Probability
6 marks
More Inverse Trigonometric Functions Maths Class 12 Resources
- Inverse Trigonometric Functions Class 12 Maths NCERT Solutions
- Inverse Trigonometric Functions Class 12 Maths Notes
- Inverse Trigonometric Functions Class 12 Maths Formula Sheet
- Inverse Trigonometric Functions Class 12 Maths NCERT Book PDF
- Inverse Trigonometric Functions Class 12 Maths NCERT Exemplar Book PDF
- Inverse Trigonometric Functions Class 12 Maths NCERT Exemplar Solutions
NCERT Handwritten Notes for Class 12 Maths: All Chapters
| Chapter | Resource |
|---|---|
| Chapter 1 | Relations and Functions Handwritten Notes |
| Chapter 3 | Matrices Handwritten Notes |
| Chapter 4 | Determinants Handwritten Notes |
| Chapter 5 | Continuity and Differentiability Handwritten Notes |
| Chapter 6 | Application of Derivatives Handwritten Notes |
| Chapter 7 | Integrals Handwritten Notes |
| Chapter 8 | Application of Integrals Handwritten Notes |
| Chapter 9 | Differential Equations Handwritten Notes |
| Chapter 10 | Vector Algebra Handwritten Notes |
| Chapter 11 | Three Dimensional Geometry Handwritten Notes |
| Chapter 12 | Linear Programming Handwritten Notes |
| Chapter 13 | Probability Handwritten Notes |
Exercise-wise Breakdown of the Inverse Trigonometric Functions Chapter
| Exercise | Topic Tested |
|---|---|
| Exercise 2.1 | Principal values of inverse trig functions |
| Exercise 2.2 | Properties and identities of inverse trig functions |
| Miscellaneous Exercise | Mixed inverse trig identities and equations |
PDF Download Formats and Languages for the Inverse Trigonometric Functions Chapter
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading, quick revision between classes | 2-3 MB |
| HD PDF | Print-ready, desk study, board hall photocopy | 8-10 MB |
| Handwritten Notes PDF | Mirrors how a topper writes the chapter under Sunday-revision pace | 5-7 MB |
- NCERT-faithful: Every definition, theorem and exercise on the inverse trigonometric functions class 12 ncert pdf matches the printed textbook line for line.
- Hindi-medium edition: The inverse trigonometric functions class 12 pdf is also available in Hindi - same page numbering, same equation labels.
- Formula PDF separate: The inverse trigonometric functions class 12 formulas pdf is a one-page A4 reference sheet listing every identity used in the chapter.
- Solutions PDF separate: The inverse trigonometric functions class 12 solutions pdf gives every NCERT exercise worked out step by step.
- State-board alignment: Students on the Maharashtra board, HSC, or any state-board syllabus will find the same definitions in this inverse trigonometric functions class 12 pdf - only the exercise numbers differ.
Important Questions and Previous Year Trends for the Inverse Trigonometric Functions Chapter
| Template | Typical Marks | What it tests |
|---|---|---|
| Proof / property verification | 3 marks | Students show that a given relation/function/expression satisfies the chapter's definitions. |
| One-step computation | 2 marks | Substitution-based item: plug into a known formula and simplify. |
| Case-study scenario | 4 marks | Real-world setup applying the chapter's definitions, introduced in CBSE 2021+ papers. |
- inverse trigonometric functions class 12 previous year questions for 2019-2024 are linked from the PYQ block at the bottom of this page - the exact CBSE phrasings.
- The inverse trigonometric functions class 12 important questions with solutions set is reused by toppers in the last fortnight of revision.
- For NCERT Exemplar practice, the matching inverse trigonometric functions class 12 extra questions set adds advanced problems suitable for JEE Main and JEE Advanced.
- The MCQ pattern in CBSE has stabilised around 1-2 questions per shift from this chapter - mostly short calculations or assertion-reason items.
Year-wise PYQ Distribution
| Year | Dominant Question Type | Approx. Marks |
|---|---|---|
| 2024 | Property verification + case-study item | 5-6 marks |
| 2023 | Computation with proof + assertion-reason MCQ | 5-6 marks |
| 2022 | Long-answer derivation + 2-mark substitution | 5-7 marks |
| 2021 | Definition recall + property check | 4-5 marks |
| 2020 | One-step computation + 3-mark proof | 5 marks |
How the Inverse Trigonometric Functions Notes Pair with NCERT Solutions and the Formula Sheet
| Resource | Use it for | When |
|---|---|---|
| Inverse Trigonometric Functions Notes (this page) | Theory, definitions, exam patterns | First pass, before practice |
| inverse trigonometric functions class 12 ncert solutions PDF | Step-by-step solved exercises | Second pass, during NCERT practice |
| inverse trigonometric functions class 12 formulas PDF | One-page identity recall | Third pass, alongside mock papers |
| Handwritten Notes PDF | Quick reading in topper's handwriting | Anytime, especially commute revision |
- The inverse trigonometric functions class 12 ncert solutions cover every back-of-chapter exercise plus the miscellaneous exercise.
- The inverse trigonometric functions class 12 solutions for each individual exercise are indexed by exercise number on the sister NCERT Solutions page (see the Exercise-wise Breakdown table above for direct links).
- The inverse trigonometric functions class 12 formulas reference sheet is the same A4 file students sometimes refer to as inverse trigonometric functions class 12 all formulas - it lists every identity used in the chapter.
- State-board references: RD Sharma, ML Aggarwal, Teachoo and the Maharashtra board inverse trigonometric functions class 12 textbook PDF all share the same core definitions.
- For class-first search phrasings - class 12 inverse trigonometric functions solutions, class 12 inverse trigonometric functions ncert solutions, ncert class 12 inverse trigonometric functions solutions - the same files cover the request.
Reference Books and State-Board Mapping
| Reference | How it maps to Inverse Trigonometric Functions Class 12 |
|---|---|
| RD Sharma Class 12 Inverse Trigonometric Functions | Question patterns overlap with NCERT at ~70%; an advanced supplement. |
| ML Aggarwal Class 12 Inverse Trigonometric Functions | Solutions style is closer to JEE; good for problem-solving practice. |
| Teachoo inverse trigonometric functions class 12 | Free online walkthroughs; useful for video-style learning. |
| Shaalaa inverse trigonometric functions class 12 solutions | State-board (Maharashtra HSC) phrasings; same core definitions. |
| Maharashtra board inverse trigonometric functions class 12 textbook PDF | Same chapter content under the HSC syllabus; exercise numbers differ. |
| NCERT Exemplar Class 12 Inverse Trigonometric Functions | Advanced problems for JEE Main/JEE Advanced preparation. |
How to Use the Inverse Trigonometric Functions Notes Page Most Effectively
| Sitting | Duration | What to do |
|---|---|---|
| Sitting 1: Theory | ~90 minutes | Read the printed NCERT chapter cover to cover. Mark every definition and theorem statement. Then read the formula recall section on this page. |
| Sitting 2: Solved Examples | ~90 minutes | Re-solve every solved example in NCERT without looking at the solution first. Compare your steps against the printed working. Use the inverse trigonometric functions class 12 ncert solutions PDF if stuck. |
| Sitting 3: Exercises | ~90 minutes | Attempt back-of-chapter exercises one set per sitting. Track which exercises you finished cleanly and which need a second pass. Click into the linked exercise pages above for verification. |
- 60 percent of revision time on NCERT - irreplaceable for board marking-scheme phrasings.
- 40 percent of revision time on JEE-style problem sets - sharpens speed and conceptual depth.
- The inverse trigonometric functions class 12 important questions set on the previous-year page is the closest free analogue to a JEE-style problem set for this chapter.
- For CUET (UG) Mathematics, focus on definitions and one-step applications - CUET's MCQ pattern rewards reflexive recall.
This Collegedunia NCERT Class 12 Mathematics page is reviewed against every CBSE board paper release.
The Collegedunia Class 12 Maths team checks every formula on this page against the printed NCERT 2026-27 edition.
Class 12 Maths Handwritten Notes PDF - Frequently Asked Questions
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