11th math Chapter 10 exercise 10.1 || Sir Ikram Raheem

Welcome to one of the most conceptual and high-scoring long questions of 11th Class Mathematics (New Book).
In this lecture, we solve Chapter 10 – Trigonometric Functions & Identities, Exercise 10.1, Question No. 6, which is based on three angles of a triangle: α, β, and γ.

This question contains multiple parts, where you are given that
α + β + γ = 180°,
and you are required to prove different trigonometric identities using this condition.

🔥 What This Question Is About

In Question No. 6, you will learn how to:
✔ Use the condition α + β + γ = 180°
✔ Convert one angle in terms of the other two
✔ Prove identities like sin(α + β), cos(β + γ), etc.
✔ Apply sum and difference formulas correctly
✔ Simplify expressions step-by-step
✔ Handle multiple parts of a long question
✔ Write neat, logical, and board-friendly proofs

This lecture makes a difficult-looking question very easy.

📐 Concepts Explained in This Lecture

✔ Angles of a triangle concept
✔ Use of α + β = 180° − γ and similar forms
✔ Application of sin(A + B) and cos(A + B) formulas
✔ Conversion of angles into standard forms
✔ Use of trigonometric identities at the right place
✔ Logical flow from LHS to RHS
✔ Common mistakes students make in exams

Every step is explained in simple language, without skipping.

🎯 Why Question No. 6 Is Extremely Important

✔ One of the most repeated long questions
✔ Appears frequently in Punjab Board exams
✔ Tests concept + identity application
✔ Carries high marks
✔ Builds confidence in triangle-based trigonometry

This lecture is equally useful for students of:
Lahore Board, Gujranwala, Faisalabad, Sahiwal, Multan, Bahawalpur, Rawalpindi, DG Khan, Sargodha & Federal Board.

🌟 Teaching Style for Every Student

This lecture is designed for:
✔ Backbenchers
✔ Average students
✔ Toppers
✔ Students who fear long trigonometric proofs

Everything is taught in an easy, slow, and exam-oriented method so that every student can write the solution in their own words.

🇵🇰 My Mission

My mission is not just to help you pass exams, but to help you understand mathematics.

• Don’t memorize identities
• Understand where and why to use them
• Develop logical thinking
• Write clean proofs
• Study with confidence
• Work for real freedom through education

This is not just a YouTube channel —
this is your classroom.

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Your success is my success.
Your learning is Pakistan’s future. 🇵🇰
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