Class 12 Maths Handwritten Notes PDF

8 pages · 7 hand-drawn graphs · 12 boxed identities · Class 12 Maths Chapter 2, 2026-27 NCERT

The Handwritten Notes on Class 12 Maths Chapter 2 Inverse Trigonometric Functions will cover all the formulas in a single PDF. The notes will help you understand the importance of formulas in solving both exemplar and in-text questions on Inverse Trigonometric Functions.

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)

Inverse Trigonometric Functions Handwritten Notes - Class 12 Maths

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.

SCAT mnemonic for inverse trig principal ranges

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

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 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 12 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

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

Other Resources

NCERT Handwritten Notes for Class 12 Maths: All Chapters

Chapter	Resource
Chapter 2	Inverse Trigonometric Functions Handwritten Notes
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

Student Feedback - 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.