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

Описание: 11th Class Mathematics | Chapter 10 – Trigonometric Functions
Exercise 10.2 | Question No. 10 (Very Very Important Long Question)

All Punjab Boards | By Sir Ikram Raheem | Learn for Pakistan

This lecture covers Exercise 10.2 – Question No. 10, one of the most important long questions of 11th class Mathematics.
This question is highly expected in board exams, and almost every Punjab Board repeats this type of question every year.

👉 Two complete parts are explained step-by-step with full logic, formulas, and concept of quadrants.

⭐ Exam Importance

✔ Very Very Important Long Question
✔ Frequently appears in annual papers
✔ High-scoring question
✔ Must prepare for board success

If you want guaranteed marks in trigonometry, this question cannot be skipped.

📐 What This Question Is About

In this question:

• Values of sin α, cos α, tan α are given
• α and β are not in the first quadrant
• Students must identify the correct quadrant
• Use basic trigonometric identities
• Prove the given expressions
• Handle square roots carefully

Sir Ikram Raheem explains why signs change in different quadrants and how to select the correct positive or negative value.

🧠 Key Concepts Covered

This lecture clearly explains:

• Concept of quadrants (I, II, III, IV)
• Which trigonometric functions are positive/negative
• Identity:
sin²θ + cos²θ = 1
• Converting identities into α:
sin²α + cos²α = 1
• Finding values using:
cos α = √(1 − sin² α)
• Logical approach instead of memorization

Everything is explained in simple words so even weak students can solve it confidently.

✍️ Board-Style Solution

You will learn:

• How to start a long question properly
• How to write step-by-step solution
• How to avoid sign mistakes
• How examiners check these questions
• How to score full marks

Perfect for students who lose marks due to small mistakes.

🏫 Valid for All Punjab Boards

This lecture is 100% useful for students of:

Lahore, Gujranwala, Faisalabad, Multan, Sahiwal, Bahawalpur, Rawalpindi, Sargodha, DG Khan, Khanewal and all Punjab Boards.

🎯 Who Should Watch?

✔ Students afraid of trigonometry
✔ Average & weak students
✔ Backbenchers
✔ Repeaters
✔ Toppers (for revision)

This lecture makes trigonometry easy and interesting.

🇵🇰 My Mission

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

My mission is:
✔ No rote learning
✔ Clear concepts
✔ Exam-focused preparation
✔ Confidence in mathematics
✔ Practical thinking
✔ Real education for Pakistan

Education is freedom, not fear.

❤️ Support Learn for Pakistan

✔ Like this lecture
✔ Subscribe to Learn for Pakistan
✔ Comment your questions — I reply personally
✔ Share with friends, colleges & academies

📘 Practice more
🧠 Understand quadrants
🇵🇰 Study for yourself, your family, and Pakistan

Sir Ikram Raheem is always with you.
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