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Double-angle Equations
Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
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Double-angle Equations
What is it?
Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
In simple words
- Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
- Worked pattern: sin2x=0 gives 2x=npi, so x=npi/2.
- Final check: domain, sign, notation, units, and reasonableness.
Important terms
Double-angle equations: Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
What you should learn
- State the rule for double-angle equations.
- Solve a double-angle equations problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
CONCEPT AND RULE
Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
METHOD
For double-angle equations, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.
WORKED EXAMPLE
sin2x=0 gives 2x=npi, so x=npi/2.
COMMON MISTAKE
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
How to solve double-angle equations
How it works
- Identify the mathematical objects, givens, restrictions, and required result.
- Choose and write the relevant definition, theorem, or formula.
- Substitute with brackets and carry out one justified step per line.
- Simplify, state the final answer clearly, and verify it in the original setting.
Remember
- Double-angle equations
- rule
- worked example
- worked example
How the ideas connect
Worked example: sin2x=0 gives 2x=npi, so x=npi/2.
Deeper understanding
Go beyond memorising Double-angle Equations. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: sin2x=0 gives 2x=npi, so x=npi/2.
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Double-angle equations
- rule
- worked example
- Double-angle equations: Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
- CONCEPT AND RULE: Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
- METHOD: For double-angle equations, identify the given information and required result. Select the matching
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
For long answers on Double-angle Equations: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Double-angle equations
- rule
- worked example
- Double-angle equations: Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
Important formulas
- Double-angle equations
- rule
- worked example
Common exam traps
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- A matching-looking formula is not valid until its conditions and domain have been checked.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- Mistake
A matching-looking formula is not valid until its conditions and domain have been checked.
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Double-angle equations
rule
worked example
Double-angle equations: Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
- Definition
- Apply sin2x, cos2x, or tan2x identities, then account for the changed angle and period.
- Critical warning
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all d
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Exam Practice
Define
Q1. Define Double-angle Equations.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Double-angle Equations and say why it fits.
Mistake
Q4. State one common mistake students make about Double-angle Equations.
Exam note
Q5. Write a short exam note on Double-angle Equations: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.