Double-angle Formulas

Double-angle Formulas

What is it?

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.

In simple words

• Put B=A.
• 2 sin cos
• cos^2-sin^2
• State the rule, show the working, and check the answer.

Important terms

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.

What you should learn

• 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.

Examples

• 2 sin cos
• cos^2-sin^2
• 2t/(1-t^2) for tan

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.

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.

Full school-level explanation

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.

Understand the idea, then apply it:

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.

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.

Remember

• B=A

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.

Remember

• focused answer
• accurate support

Examples

• State the central idea
• Use one accurate detail
• Check the final response

How to answer a double-angle formulas question

How it works

• 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.

Remember

• B=A
• tan(A+B)=s+t1-st
• sin 2A = 2 sin A cos A
• minus in tan(A+B) bottom
• B=A
• focused answer
• accurate support
• B=A

Deeper understanding

Go beyond memorising Double-angle Formulas. Connect the definition to reasons, relationships, exceptions, and exam wording.

Common mistakes

Exam focus

Core Idea

What to Know

Example or Evidence

How to Answer

Exam focus

Quick revision

• B=A
• tan(A+B)=s+t1-st
• sin 2A = 2 sin A cos A
• minus in tan(A+B) bottom
• 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). H
• DOUBLE: Put B=A.

Bottom 1 - tan A tan B. If you write 1 + by accident, A+B is wrong.

For long answers on Double-angle Formulas: define clearly → explain the main parts → give one example → state one exam caution.