Exercise 10.2 Solutions - Class 11 Mathematics Unit 10 Trigonometric Identities

Step-by-step solved problems and identity proofs for Exercise 10.2, Unit 10: Trigonometric Identities.Comprehensive solutions covering sum and difference formulas, non-standard angle evaluations, and basic identity proofs for Punjab Board Class 11 (PCTB).

This page provides comprehensive, step-by-step solved solutions for Exercise 10.2 of Unit 10: Trigonometric Identities for Class 11 Mathematics under the Punjab Board (PCTB / PECTAA). All problems involving compound angle formulas sin(α ± β), cos(α ± β), tan(α ± β), evaluation of exact trigonometric values for angles like 15°, 75°, 105°, identity verifications, and harmonic conversion to r sin(θ + φ) are fully resolved for HSSC Part 1 examination prep.
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Exercise Overview

Exercise 10.2 expands upon the fundamental angle identities in Unit 10: Trigonometric Identities in Class 11 Mathematics, demonstrating advanced algebraic manipulations and proof strategies for compound angle relations.

The exercise trains students in three core problem types: evaluating exact surd values for non-standard angles (such as 15°, 75°, and 105°) by decomposing them into known standard angles (30°, 45°, 60°); verifying intricate trigonometric identities involving multiple terms and rational functions; and converting linear combinations of the form a sin θ + b cos θ into single harmonic sinusoids r sin(θ + φ) or r cos(θ - φ) using auxiliary polar substitutions.

In Punjab Board HSSC Part 1 examinations, Exercise 10.2 is a vital source of Section B short questions and Section C long questions across Lahore, Rawalpindi, Gujranwala, Faisalabad, Multan, and other BISE boards. Mastering these step-by-step proofs builds strong analytical competence essential for subsequent units on double and half angles, inverse trigonometry, and calculus.

FAQs

Are these Exercise 10.2 solutions according to the Punjab Board syllabus?
Yes, these solutions strictly follow the official Punjab Curriculum and Textbook Board (PCTB / PECTAA) Class 11 Mathematics syllabus for Unit 10 (Trigonometric Identities) for the 2026-2027 academic session.
What are the key concepts covered in Exercise 10.2 Class 11 Mathematics?
Exercise 10.2 covers further applications of basic identities, including compound angle expansions, non-standard angle evaluations (15°, 75°, 105°), identity verifications, and converting expressions into r sin(θ + φ) form.
How are compound angle identities used to evaluate non-standard angles like 15° and 75°?
Non-standard angles are split into combinations of standard angles (45° - 30° = 15° or 45° + 30° = 75°), allowing exact radical values to be calculated using sin(α ± β), cos(α ± β), and tan(α ± β) without a calculator.
What are the primary sum and difference identities for sine, cosine, and tangent?
Key identities include sin(α ± β) = sin α cos β ± cos α sin β, cos(α ± β) = cos α cos β ∓ sin α sin β, and tan(α ± β) = (tan α ± tan β) / (1 ∓ tan α tan β).
How do you express a sin θ + b cos θ in the harmonic form r sin(θ + φ)?
Set r = √(a² + b²) and φ = tan⁻¹(b/a). Dividing by r and substituting cos φ = a/r and sin φ = b/r reduces the linear combination to r sin(θ + φ).
Can students read these Exercise 10.2 solutions online?
Yes, students can read all step-by-step proofs and solved questions for Exercise 10.2 directly online on MaryamNotes.pk on any web browser without needing to download files.
Are these identity proofs important for Punjab Board Class 11 examinations?
Yes, identity proofs from Exercise 10.2 are core fixtures of Section B short questions and Section C long questions across all BISE Punjab boards.
Are these Class 11 Exercise 10.2 notes completely free to access?
Yes, all solved notes, identity derivations, and practice solutions on MaryamNotes.pk are 100% free and open to all students and educators.