MathematicsChapter 8: Fundamentals of Trigonometry
Double-Angle Formulas
Put B=A. Three forms of cos 2A are all useful (pick the one that matches sin or cos on the paper).
Learning objectives
- State the rule or meaning of double-angle formulas in easy words.
- Apply double-angle formulas in a clear step-by-step solution.
- Check the conditions, working, and final answer for accuracy.
Definition
Put B=A. Three forms of cos 2A are all useful (pick the one that matches sin or cos on the paper). Half-angle later if asked via rearranging cos 2A.
Formula
B=A. Three forms of cos 2A are all useful
Where / symbols
- DOUBLE-ANGLE FORMULAS
- Put B=A. Three forms of cos 2A are all useful (pick the one that matches sin or cos on the paper). Half-angle later if asked via rearranging cos 2A.
- DOUBLE
- Put B=A.
Relationship
- B=A
- tan(A+B)=s+t1-st
- sin 2A = 2 sin A cos A
Overview
Understand the idea, then apply it:
Main Idea
Put B=A. Three forms of cos 2A are all useful (pick the one that matches sin or cos on the paper). Half-angle later if asked via rearranging cos 2A.
Examples 2 sin cos · cos^2-sin^2 · 2t/(1-t^2) for tan
Exam Use
Write the rule first: Put B=A. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Examples State the central idea · Use one accurate detail · Check the final response
WHAT — DOUBLE-ANGLE FORMULAS
Put B=A. Three forms of cos 2A are all useful (pick the one that matches sin or cos on the paper). Half-angle later if asked via rearranging cos 2A.
WHY — Why it matters
This rule is a separate learning unit inside tan(a±b) and double angle. It can be defined, applied, and checked in its own FBISE question.
HOW — How to answer
Write the rule first: Put B=A. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
How to answer a double-angle formulas question
- Read the exact command word and identify what the question asks.
- State the matching idea, rule, or meaning before adding detail.
- Use the unit evidence or mathematical working that directly supports the answer.
- Check accuracy, relevance, and answer length before finishing.
In simple words
Bottom 1 - tan A tan B. If you write 1 + by accident, A+B is wrong.
Key points
- B=A
- tan(A+B)=s+t1-st
- sin 2A = 2 sin A cos A
- focused answer
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Double-Angle Formulas
Sticky Notes · Quick Revision
Core Idea
- Put B=A.
What to Know
- Put B=A. Three forms of cos 2A are all useful (pick the one that matches sin or cos on the paper). Half-angle later if asked via rearranging cos 2A.
Example or Evidence
- 2 sin cos
- cos^2-sin^2
- 2t/(1-t^2) for tan
How to Answer
- Write the rule first: Put B=A. Substitute carefully, show one step per line, and check signs, restrictions, units, and the final result.
Common Error
- Bottom 1 - tan A tan B. If you write 1 + by accident, A+B is wrong.
FBISE Exam Check
- State the rule, show the working, and check the answer.
60-second revision
- Put B=A.
- 2 sin cos
- cos^2-sin^2
- State the rule, show the working, and check the answer.
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