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

Описание: 11th Class Mathematics | Chapter 10 Trigonometry | Exercise 10.2 Question 15 (All 6 Parts) | Express in r sin(θ ± φ) | Easy Method | Learn for Pakistan

In this lecture, Sir Ikram Raheem teaches 11th Class Mathematics Chapter 10 Trigonometric Functions and Identities from the new book (2025 onward syllabus).
This lecture covers Exercise 10.2 Question Number 15 (All Six Parts) which is a very important short question for all Punjab Boards including Lahore, Gujranwala, Sahiwal, Multan, Bahawalpur, Rawalpindi, Sialkot and all other boards.

⭐ This question is exam-focused and mostly comes in board papers.

📘 Main Topic of This Lecture

Express the following in the form:
✔ r sin(θ + φ)
✔ r sin(θ − φ)
✔ r cos(θ + φ)
✔ r cos(θ − φ)

Example type question:
👉 24 sinθ + 7 cosθ
👉 And remaining five similar parts solved step by step

📚 Concepts Covered

In this lecture you will learn:

✅ How to convert a sinθ + b cosθ into R sin(θ ± φ)
✅ How to find value of R using formula
👉 r = √(a² + b²)

✅ How to find angle φ
✅ Trigonometric identity concept
✅ Step by step board pattern solving
✅ Easy method for weak students

🧠 Why This Question Is Important

✔ Very Important Short Question
✔ Helps in Long Questions Also
✔ Improves Concept of Trigonometry
✔ Important for Entry Tests + Board Exams
✔ Helps in Physics Applications Also

👨‍🎓 Best For

✔ Toppers — For Full Marks
✔ Average Students — For Concept Building
✔ Backbenchers — For Easy Understanding

Sir Ikram Raheem teaches in Simple Urdu + Easy English, so students can understand easily and write answers confidently in exams.

🇵🇰 My Mission – Learn for Pakistan

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My Mission is:
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⭐ Logical Thinking Development
⭐ Help Weak Students Pass
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📢 Student Action

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Thank You For Watching ❤️
Sir Ikram Raheem
Learn for Pakistan