11th math Chapter 10 exercise 10.2 || Sir Ikram Raheem

11th Class Mathematics | Chapter 10 – Trigonometric Identities
Exercise 10.2 | Question No. 1 (Very Important Short Question)

New Book | Easy Method | Sir Ikram Raheem | Learn for Pakistan

Welcome to one of the most important and high-scoring topics of 11th Class Mathematics (New Book).
In this lecture, Sir Ikram Raheem explains Chapter 10, Exercise 10.2, Question No. 1 in a simple, logical, and exam-oriented method that every student can understand and practice easily.

🔑 What This Question Is About

In this question, we find the exact values of:
• sin 15°
• cos 15°
• cos 105°

👉 Without using a calculator, using angle sum and difference formulas.

🧠 Given Hints Used in This Lecture

✔ 15° = 45° − 30°
✔ 105° = 60° + 45°

Using:
• sin(A − B)
• cos(A − B)
• cos(A + B)

All formulas are explained step-by-step so that students never forget them in exams.

⭐ Why This Question Is Extremely Important

✔ Repeated in short questions
✔ Common in annual exams
✔ Tests concept clarity, not memorization
✔ Easy marks if method is clear
✔ Builds strong base for Exercise 10.2

This question is guaranteed exam-focused for all Punjab Boards.

✍️ Easy Method – Special for Weak & Average Students

This lecture is designed for:
• Backbenchers
• Average students
• Students afraid of trigonometry
• Students who forget formulas

Sir Ikram Raheem explains:
✔ Why we split angles
✔ How formulas work
✔ Which sign is positive in which quadrant
✔ How to write steps properly in exams

So you can solve confidently and score maximum marks.

🏫 Valid for All Punjab Boards

This lecture is 100% applicable for:
Lahore Board, Gujranwala, Sahiwal, Khanewal, Multan, Bahawalpur, Faisalabad, DG Khan, Rawalpindi, Sargodha & all Punjab Boards.

🇵🇰 My Mission – Real Change in Education

My mission is not just to help students pass exams.

❌ No rote learning
❌ No blind memorization

✅ Concept-based learning
✅ Practical thinking
✅ Skill-based & digital education
✅ Confidence in mathematics
✅ Real change in Pakistan’s education system

This channel is not entertainment —
this is a movement for real education.

📢 Join This Learning Mission

✔ Subscribe for complete chapter coverage
✔ Like to support free quality education
✔ Comment your questions — I reply personally
✔ Share with friends, academies & classmates

Study for yourself
Study for your family
Study for Pakistan 🇵🇰
#LearnForPakistan #SirIkramRaheem #11thClassMath #NewMathBook2025 #ComplexNumbers #Z1Z2 #EasyMathMethod #PunjabBoard #BoardExamPreparation #MathInUrdu #MathematicsMadeEasy #EducationForPakistan #MotivationalLearning #PracticalEducation