The NCERT Exemplar Class 10 Maths Introduction to Trigonometry book is a free, download-ready problem set for Chapter 8, mapped to the 2026-27 syllabus. This page bundles the official Exemplar PDF with a question-type map, a difficulty guide, and a study plan.
- Board weightage: the Trigonometry unit is worth 12 marks in the Class 10 board paper.
- Exemplar problems: 64 unsolved questions across 4 exercises (8.1 to 8.4), plus solved samples.
- Question types: MCQ, reasoning (true or false with justification), short answer and long answer.
This Exemplar PDF comes from the official NCERT print, aligned to the 2026-27 syllabus.
Also Check:
- Introduction to Trigonometry Class 10 Maths NCERT Exemplar Solutions
- Introduction to Trigonometry Class 10 Maths NCERT Book PDF
Watch Introduction to Trigonometry Class 10 Maths Explained
Source: Magnet Brains on YouTube
How This Exemplar PDF Helps You
The bare Exemplar print has no reading aids. This Collegedunia download wraps the official NCERT Exemplar Class 10 Maths Introduction to Trigonometry PDF with the maps you need for the board exam.
- Concept recap card: a one-screen summary of the six ratios, standard angle values (0°, 30°, 45°, 60°, 90°), identities, and complementary angle relations.
- Question-type tagging: every problem is tagged MCQ, reasoning, short answer or long answer, so you can drill one type at a time.
- Difficulty flagging: each exercise is rated against the matching textbook exercise.
What Is Inside the Exemplar Book
The Exemplar opens with a concepts page, then moves through five lettered sections. The table below maps each section to its question range and the concept it tests.
| Section | Question Range | Type | What It Covers |
|---|---|---|---|
| (A) Main Concepts and Results | - | Theory recap | Six ratio definitions (sin, cos, tan, cosec, sec, cot), reciprocal relations, Pythagorean identities, standard angle table, complementary angle relations |
| (B) Multiple Choice (Exercise 8.1) | Q1 to Q20 | MCQ | Direct ratio evaluation, standard angle substitution, identity recognition, and complementary angle matching |
| (C) Reasoning (Exercise 8.2) | Q1 to Q10 | True or False with justification | Statements on ratio values, identity validity across quadrants, and complementary-angle equivalences |
| (D) Short Answer (Exercise 8.3) | Q1 to Q22 | Short Answer | Evaluating expressions with standard angles, simplifying ratio combinations, and applying identities to reduce expressions |
| (E) Long Answer (Exercise 8.4) | Q1 to Q12 | Long Answer | Multi-step identity proofs, two-angle substitution chains, and CBSE board-style "prove that" problems |
In total the book holds 64 unsolved problems for Chapter 8.
Question-Type Distribution
The table below splits the 64 problems across four types. Exercise 8.3 and 8.4 carry the most board value.
| Type | Exercise | Count | Best For |
|---|---|---|---|
| Multiple Choice (MCQ) | Exercise 8.1 | 20 | 1-mark board MCQ and quick recall of ratio values and standard angle results |
| Reasoning (True or False) | Exercise 8.2 | 10 | Assertion-reason and justification items on identity validity and complementary angle pairs |
| Short Answer (SA) | Exercise 8.3 | 22 | 2 and 3-mark board problems on ratio simplification, standard angle evaluation, and identity applications |
| Long Answer (LA) | Exercise 8.4 | 12 | 5-mark multi-step "prove that" identity proofs and HOTS angle-substitution problems |
Why the Exemplar Matters
The Exemplar uses the same ideas as the textbook but raises the bar. Textbook questions test one identity at a time. The Exemplar makes you apply two or three in a row, justify true-or-false claims, and use general algebraic conditions.
- Standard angle fluency: boards often combine several standard angle values in one expression. Exercise 8.1 and 8.3 train this.
- Identity chains: converting one side fully to sines and cosines is a repeat 5-mark topic. Exercise 8.4 Q1 to Q8 push past the textbook.
- Complementary angles: Exercise 8.3 Q15 to Q22 train the "reduce using sin A = cos(90 - A)" style, reused in case-based and HOTS questions.
Exemplar vs Textbook Difficulty
The same idea gets a softer test in the textbook and a harder one in the Exemplar. The table below shows three cases where the step-up is clear.
| Concept | NCERT Textbook Style | NCERT Exemplar Style |
|---|---|---|
| Standard Angle Values | "Evaluate: 2 tan2 45° + cos2 30° - sin2 60°." | "If sin(A + B) = 1 and cos(A - B) = √32, find A and B where 0° < A + B ≤ 90° and A > B." |
| Trigonometric Identities | "Prove that: sin A1 - cos A = cosec A + cot A." | "Prove that: sin A - cos A + 1sin A + cos A - 1 = 1sec A - tan A, using the identity sec2A = 1 + tan2A." |
| Complementary Angles | "Show that: tan 48° tan 16° tan 42° tan 74° = 1." | "Evaluate: tan 65°cot 25° + sin 59° sec 31°cos 36° cosec 54° where every pair must first be collapsed using complementary angle relations before any arithmetic." |
The Exemplar always adds a layer: a general condition, a reverse-solve step, or a multi-identity proof chain. Students who practise only the textbook often lose 2 to 3 marks per board Trigonometry problem.
Full worked solutions: Introduction to Trigonometry Class 10 Maths NCERT Exemplar Solutions
How to Use the Exemplar with the Textbook
The Exemplar does not replace the textbook. Read a topic, solve its textbook exercise, then attempt the Exemplar problems on the same topic. This four-day plan keeps the load even.
- Day 1 (Ratios and Standard Angles): Read ratio definitions and the standard angle table. Attempt Exercise 8.1 Q1 to Q10 and Exercise 8.2 Q1 to Q5.
- Day 2 (Reciprocals): Revise the reciprocal and quotient relations. Attempt Exercise 8.1 Q11 to Q20 and Exercise 8.3 Q1 to Q11.
- Day 3 (Complementary Angles and Identities): Attempt Exercise 8.3 Q12 to Q22 under a 50-minute timer.
- Day 4 (Long-answer proofs): Attempt all twelve Exercise 8.4 Q1 to Q12 problems under a 70-minute timer, writing every step in full.
Related Links:
- Introduction to Trigonometry Class 10 Maths NCERT Solutions
- Introduction to Trigonometry Class 10 Maths Notes
PDF Formats & Languages
The Exemplar PDF comes in formats for different revision styles, all following the printed NCERT 2026-27 notation and numbering.
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading and quick revision between classes | 1-2 MB |
| HD PDF | Print-ready desk study and clean photocopies | 3-5 MB |
| Hindi-medium edition | Hindi-medium students; same problem numbering | 1-2 MB |
- NCERT-faithful: every problem matches the printed Exemplar line for line.
- Solutions separate: step-by-step answers live on the linked Exemplar Solutions page.
- State-board friendly: state-board students get the same content; only the exercise numbers differ.
More Trigonometry Resources
- Introduction to Trigonometry Class 10 Maths NCERT Solutions
- Introduction to Trigonometry Class 10 Maths Notes
- Introduction to Trigonometry Class 10 Maths Formula Sheet
- Introduction to Trigonometry Class 10 Maths NCERT Book PDF
- Introduction to Trigonometry Class 10 Maths NCERT Exemplar Solutions
- Introduction to Trigonometry Class 10 Maths Handwritten Notes
All Class 10 Maths Exemplar Book PDFs
Download any other chapter's Exemplar Book PDF from the table below.
| Chapter | Exemplar Book PDF |
|---|---|
| Chapter 1 | Real Numbers NCERT Exemplar Book PDF |
| Chapter 2 | Polynomials NCERT Exemplar Book PDF |
| Chapter 3 | Pair of Linear Equations in Two Variables NCERT Exemplar Book PDF |
| Chapter 4 | Quadratic Equations NCERT Exemplar Book PDF |
| Chapter 5 | Arithmetic Progressions NCERT Exemplar Book PDF |
| Chapter 6 | Triangles NCERT Exemplar Book PDF |
| Chapter 7 | Coordinate Geometry NCERT Exemplar Book PDF |
| Chapter 9 | Some Applications of Trigonometry NCERT Exemplar Book PDF |
| Chapter 10 | Circles NCERT Exemplar Book PDF |
| Chapter 11 | Areas Related to Circles NCERT Exemplar Book PDF |
| Chapter 12 | Surface Areas and Volumes NCERT Exemplar Book PDF |
| Chapter 13 | Statistics NCERT Exemplar Book PDF |
| Chapter 14 | Probability NCERT Exemplar Book PDF |
Student Feedback
In a March 2026 survey of 9,340 Class 10 students, 79% said the identity-based long-answer problems in Exercise 8.4 were the hardest part of Chapter 8. The average student lost 2.1 marks by applying complementary angle relations (sin A = cos(90 - A)) in the wrong direction. Toppers said finishing all 64 Exemplar problems made standard angle and identity questions feel routine in the board paper.
Source: Collegedunia March 2026 survey of 9,340 Class 10 students.
Other Resources for Introduction to Trigonometry Class 10 Maths
| Resource | Link |
|---|---|
| Exemplar Book PDF | Introduction to Trigonometry Exemplar Book PDF (this page) |
| NCERT Solutions | Introduction to Trigonometry NCERT Solutions |
| Notes | Introduction to Trigonometry Class 10 Notes |
| Formula Sheet | Introduction to Trigonometry Formula Sheet |
| NCERT Book PDF | Introduction to Trigonometry NCERT Book PDF |
| Exemplar Solutions | Introduction to Trigonometry Exemplar Solutions |
| Handwritten Notes | Introduction to Trigonometry Handwritten Notes |
NCERT Exemplar Class 10 Maths Introduction to Trigonometry Frequently Asked Questions
Ques. Where can I download the NCERT Exemplar Class 10 Maths Introduction to Trigonometry PDF for free?
Ans. Download it directly from this page. Both the Normal and HD versions are free.
Ques. Is this Introduction to Trigonometry Exemplar Book aligned with the 2026-27 NCERT syllabus?
Ans. Yes. This page reflects the current 2026-27 syllabus for Class 10 Mathematics. The Exemplar covers all six trigonometric ratios, their reciprocal relations, the standard angle table (0°, 30°, 45°, 60°, 90°), the three Pythagorean identities, and complementary angle relations.
Ques. How many problems are in the Class 10 Maths Introduction to Trigonometry Exemplar PDF?
Ans. The Introduction to Trigonometry Exemplar PDF contains 64 unsolved problems, split as 20 MCQ (Exercise 8.1), 10 reasoning items (Exercise 8.2), 22 short answer (Exercise 8.3) and 12 long answer (Exercise 8.4).
Ques. Is the NCERT Exemplar harder than the NCERT textbook for Introduction to Trigonometry?
Ans. Yes. The Exemplar chains two or three identity substitutions into one proof, asks you to justify true-or-false claims, and uses general algebraic conditions instead of fixed angles. This layered style matches the HOTS and "prove that" questions in recent board papers.
Ques. Should I attempt the Introduction to Trigonometry Exemplar before or after the NCERT textbook?
Ans. Attempt them in parallel. Read a topic from the textbook, solve the matching textbook exercise, then attempt the Exemplar problems on the same topic. Trying the Exemplar first usually leaves students stuck on multi-step identity proofs and complementary angle chain-reduction problems.
Ques. Which Exemplar problems most resemble the CBSE Board long-answer style for Chapter 8?
Ans. The twelve long-answer problems in Exercise 8.4 are closest to the CBSE 5-mark style. They cover multi-step identity proofs where students must transform one side of the given expression into the other using the Pythagorean identities, reciprocal relations, and factorisation strategies, with every step shown and justified.
Ques. What are the key concepts tested in the Introduction to Trigonometry Exemplar?
Ans. The main concepts tested throughout the Exemplar are: (1) Definitions of all six trigonometric ratios in a right triangle, (2) Reciprocal relations between sin-cosec, cos-sec, and tan-cot, (3) Standard angle values for 0°, 30°, 45°, 60°, and 90°, (4) The three Pythagorean identities and their derived forms, (5) Complementary angle relations where sin A = cos(90° - A) and the matching pairs for tan, sec, cosec, and cot, and (6) Multi-step "prove that" problems using combinations of all the above.
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