Introduction
The best Unit 10, Trigonometric Identities, solved notes for Class 11 Punjab Boards are now available, with 100 percent of exercises solved using easy, step by step solutions and the marking scheme, based on the new book from PECTAA, the Punjab Curriculum and Textbook Board.
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These notes are perfect for the 2026 exams and are built to help students score 90 plus marks.
Ideal for Students, Teachers, and Lecturers Across All Nine Punjab Boards
These notes are used at top registered institutions across all nine Punjab boards, including Aitchison College Lahore (Lahore Board), Sadiq Public School Bahawalpur (Bahawalpur Board), Army Public Schools (Rawalpindi and Multan Boards), Beaconhouse Schools (Faisalabad and Gujranwala Boards), Forman Christian College Lahore (Lahore Board), Government College University Faisalabad (Faisalabad Board), Cadet College Hasan Abdal (Rawalpindi Board), Cadet College Petaro.
Cadet College Okara (Sahiwal Board), Cadet College Kohat, Cadet College Sargodha (Sargodha Board), Cadet College Jhang (Faisalabad Board), Cadet College Pasrur (Gujranwala Board), Cadet College Spinkai (DG Khan Board), Military College Jhelum (Rawalpindi Board), Garrison Cadet College Kohat, and many more.
What’s Inside Unit 10, Building Identities From the Unit Circle Up
Unit 10 takes the trig ratios students already know and stretches them across the full range of angles, positive, negative, and beyond 360 degrees, before turning them into tools for proving identities and combining angles.
It opens with trigonometric values without tables, using reference angles, periodicity, and the signs of trig ratios in each quadrant to evaluate expressions involving negative angles and angles well outside the standard 0 to 360 degree range, all without a calculator or table.
From there, the unit moves into fundamental identities and their proofs, covering the Pythagorean identities, reciprocal and quotient identities, and how to prove more complex identities by simplifying one side to match the other or working both sides toward a common form.
The sum and difference formulas follow, covering sin(A ± B), cos(A ± B), and tan(A ± B), along with how these are used to find exact values of angles like 15° or 75° by writing them as a sum or difference of standard angles.
The unit then covers double angle and half angle identities, deriving sin 2A, cos 2A, and tan 2A from the sum formulas, along with the half angle versions used when an angle needs to be split rather than combined.
It closes with product to sum and sum to product identities, which convert between a product of two trig functions and a sum or difference, a conversion that becomes essential for solving certain trigonometric equations and simplifying expressions that don’t reduce any other way.
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Exercise 10.1, Trigonometric Values Without Tables, Fully Solved
All questions in Exercise 10.1 are fully solved, covering evaluating trig ratios for negative angles and angles beyond one full rotation using periodicity and reference angles.
| Question | Expression | Result |
|---|---|---|
| Q1(i) | cos(−1230°) | −√3/2 |
| Q1(ii) | tan(−1035°) | 1 |
| Q1(iii) | sec(1140°) | 2 |
| Q1(iv) | csc(−690°) | 2 |
The full solved PDF for Exercise 10.1 is available, covering every question and part in complete detail.
Exercise 10.2, Fundamental Identities and Proofs, Fully Solved
Exercise 10.2 is fully solved, covering proofs built from the Pythagorean, reciprocal, and quotient identities, including the trickier proofs that require simplifying both sides toward a common middle expression.
Exercise 10.3, Sum and Difference Formulas, Fully Solved
Exercise 10.3 is fully solved, covering the expansion of sin, cos, and tan for a sum or difference of angles, and using these formulas to find exact values for non-standard angles built from standard ones.
Exercise 10.4, Double Angle and Half Angle Identities, Fully Solved
Exercise 10.4 is fully solved, covering the derivation and application of double angle formulas for sin, cos, and tan, along with half angle identities used in simplification and equation solving.
Exercise 10.5, Product to Sum and Sum to Product Identities, Fully Solved
Exercise 10.5 is fully solved, covering converting between products and sums of trig functions in both directions, and applying these conversions to simplify expressions and solve equations.
Review Exercise, Unit 10, Fully Solved
The Review Exercise for Unit 10 is fully solved, mixing questions from across all five exercises into exam style problems that test whether the right identity is chosen for the right situation.
Bonus Resources
- A Trigonometric Identities formula sheet PDF for quick reference.
- The top 30 periodicity and reference angle shortcuts for faster problem solving.
- Trigonometric Identities video lectures.
Why This Unit Matters for Your Overall Score
Trigonometric Identities is one of the units where a shaky foundation shows up immediately, since every later exercise assumes the reference angle and periodicity work from Exercise 10.1 is already solid.
Getting comfortable with the fundamental identities in Exercise 10.2 before moving to the sum, difference, double, and half angle formulas in Exercises 10.3 and 10.4 makes those derivations feel like natural extensions rather than a fresh set of formulas to memorize. The product to sum conversions in Exercise 10.5 tend to be underpracticed, but they show up often enough in the Review Exercise and past papers that spending extra time there is one of the highest leverage moves available in this unit.
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Frequently Asked Questions
Which exercises are covered in these Unit 10 notes?
Exercise 10.1 through Exercise 10.5 are covered in full, along with the Unit 10 Review Exercise, spanning trig values without tables, fundamental identity proofs, sum and difference formulas, double and half angle identities, and product to sum conversions.
How do I evaluate a trig ratio for an angle beyond 360 degrees without a table?
Reduce the angle to its reference angle by subtracting or adding multiples of 360 degrees, then use the sign of the trig function in the resulting quadrant to attach the correct positive or negative sign to the reference angle’s value.
Conclusion
With Exercise 10.1 through Exercise 10.5 and the Review Exercise fully solved, Class 11 students across all nine Punjab boards have a complete, exam ready resource for mastering Trigonometric Identities ahead of the 2026 exams. Use these notes alongside the bonus formula sheet, shortcuts, and past papers to build both speed and accuracy for your Mathematics exam.
Best of luck for your Class 11 Mathematics exam!