Topic explanation

Standard explanation

Squaring can introduce roots; dividing by a trig factor can lose roots. Substitute into the original equation.

Key points

• Extraneous and lost solutions
• rule
• worked example
• Extraneous and lost solutions: Squaring can introduce roots; dividing by a trig factor can lose roots. Substitute into the original
• CONCEPT AND RULE: Squaring can introduce roots; dividing by a trig factor can lose roots. Substitute into the original
• METHOD: For extraneous and lost solutions, identify the given information and required result. Select the ma
• Squaring can introduce roots; dividing by a trig factor can lose roots. Substitute into the original equation.
• Worked pattern: Never divide by sin x before separately testing sin x=0.

Labelled diagram