MathematicsChapter 9: Solution of Trigonometric Equations
Equations Reducible By Factoring
Move all terms to one side, factor, and solve every factor without dividing away solutions.
Learning objectives
- State the rule for equations reducible by factoring.
- Solve a equations reducible by factoring problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Move all terms to one side, factor, and solve every factor without dividing away solutions.
Mathematical form
x=0 gives sin x
x=12.
Where / symbols
- Equations reducible by factoring
- Move all terms to one side, factor, and solve every factor without dividing away solutions.
CONCEPT AND RULE
Move all terms to one side, factor, and solve every factor without dividing away solutions.
METHOD
For equations reducible by factoring, 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
2sin x cos x-sin x=0 gives sin x=0 or cos x=12.
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 equations reducible by factoring
- 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:
- 2sin x cos x-sin x=0 gives sin x=0 or cos x=12.
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
- Equations reducible by factoring
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Equations Reducible By Factoring
Sticky Notes · Formula and Worked Revision
Core Idea
- Move all terms to one side, factor, and solve every factor without dividing away solutions.
Rule / Formula
- Move all terms to one side, factor, and solve every factor without dividing away solutions.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- 2sin x cos x-sin x=0 gives sin x=0 or cos x=12.
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
- Move all terms to one side, factor, and solve every factor without dividing away solutions.
- Worked pattern: 2sin x cos x-sin x=0 gives sin x=0 or cos x=12.
- Final check: domain, sign, notation, units, and reasonableness.
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