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A-LevelMathematicsTrigonometry9709/12 · Oct/Nov 2010 · Q24 Marks

Prove the identity tan²x - sin²x = tan²x sin²x.

  1. Prove the identity tan²x - sin²x = tan²x sin²x.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2010). The mark or mark type is shown in brackets.

  1. [M1] LHS = sin²x/cos²x - sin²x
  2. Replace t² by s²/c² or sec² – 1
  3. [M1] sin²x(1 – cos²x)/cos²x
  4. Use of 1 - cos²x = sin²x
  5. [M1] sin²x sin²x / cos²x
  6. Valid overall method
  7. [A1] tan²xsin²x AG
  8. OR RHS = sin²x/cos²x . sin²x
  9. [M1] Replace t² by s²/c2
  10. [M1] sin²x(1 – cos²x)/cos²x
  11. Use of 1 - cos²x = sin²x
  12. [M1] (sin²x/cos²x) - sin²x
  13. Valid overall method
  14. [A1] tan²x - sin²x AG

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source
A-Level Mathematics, Oct/Nov 2010 Paper 1 Variant 2, question 2.

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