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A-LevelMathematicsTrigonometry9709/33 · May/June 2020 · Q56 Marks

By first expressing the equation tan θ tan(θ + 45°) = 2 cot 2θ as a quadratic equation in tan θ, solve the equation for 0° < θ < 90°.

  1. By first expressing the equation tan θ tan(θ + 45°) = 2 cot 2θ as a quadratic equation in tan θ, solve the equation for 0° < θ < 90°.[6]

Mark scheme

Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.

  1. [M1] Use tan 2A formula to express RHS in terms of tan θ
  2. [M1] Use tan (A + B) formula to express LHS in terms of tan θ
  3. [A1] Using tan 45° = 1, obtain a correct horizontal equation in any form
  4. [A1] Reduce equation to 2 tan² θ + tan θ - 1 = 0
  5. [M1] Solve a 3-term quadratic and find a value of θ
  6. [A1] Obtain answer θ = 26.6° and no other

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, May/June 2020 Paper 3 Variant 3, question 5.

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