MathematicsChapter 9: Solution of Trigonometric Equations
Using Fundamental Identities
Use sin^2x+cos^2x=1 or related identities to express an equation in one function.
Learning objectives
- State the rule for using fundamental identities.
- Solve a using fundamental identities problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Use sin^2x+cos^2x=1 or related identities to express an equation in one function.
Formula
cos2x=0.
Where / symbols
- Using fundamental identities
- Use sin^2x+cos^2x=1 or related identities to express an equation in one function.
CONCEPT AND RULE
Use sin^2x+cos^2x=1 or related identities to express an equation in one function.
METHOD
For using fundamental identities, 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
cos2x=sin2x gives cos2x=0.
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 using fundamental identities
- 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.
Worked example
- Worked example:
- cos2x=sin2x gives cos2x=0.
In simple words
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Key points
- Using fundamental identities
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Using Fundamental Identities
Sticky Notes · Formula and Worked Revision
Core Idea
- Use sin^2x+cos^2x=1 or related identities to express an equation in one function.
Rule / Formula
- Use sin^2x+cos^2x=1 or related identities to express an equation in one function.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- cos2x=sin2x gives cos2x=0.
Common Error
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
FBISE Exam Tip
- Show the formula, substitutions, algebra, restrictions, and final answer; method marks need visible reasoning.
60-second revision
- Use sin^2x+cos^2x=1 or related identities to express an equation in one function.
- Worked pattern: cos^2x=sin^2x gives cos2x=0.
- Final check: domain, sign, notation, units, and reasonableness.
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