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A-LevelMathematicsTrigonometry9709/21 · May/June 2024 · Q47 Marks

Show that 3 tan 2θ+ tan(θ+45°) = tan²θ+8 tanθ+1 1-tan²θ

  1. (a)Show that 3 tan 2θ+ tan(θ+45°) = tan²θ+8 tanθ+1 1-tan²θ[4]
  2. (b)Hence solve the equation 3 tan 2θ+ tan(θ+45°) = 4 for 0° < θ < 180°.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

  1. [B1] State 3 tan 2θ = 6 tan θ / (1-tan²θ)
  2. [B1] State tan(θ+45°) = (tan θ + 1) / (1-tan θ)
  3. [M1] Attempt to express left-hand side in terms of tan θ as a single fraction
  4. [A1] Confirm (tan²θ+8 tan θ+1)/(1-tan²θ)
  5. [M1] Solve quadratic equation 5tan²θ+8 tan θ-3=0 to obtain at least one value of θ
  6. [A1] Obtain 17.4
  7. [A1] Obtain 117.6

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source
A-Level Mathematics, May/June 2024 Paper 2 Variant 1, question 4.

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