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A-LevelMathematicsTrigonometry9709/21 · Oct/Nov 2025 · Q45 Marks

Solve the equation cotθ tan(θ+45°) = 7 for 0° < θ < 90°.

  1. Solve the equation cotθ tan(θ+45°) = 7 for 0° < θ < 90°.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

  1. [M1*] Attempt to express equation in terms of tanθ only
  2. [A1] Obtain 1/tanθ × (tanθ + tan45)/(1 − tanθ tan45) = 7 OE
  3. [A1] Simplify to obtain equation 7tan²θ − 6tanθ + 1 = 0
  4. [DM1] Attempt solution of three-term quadratic equation in tanθ to obtain at least one value of θ
  5. [A1] Obtain tanθ = (3 ± √2)/7 or equivalent and hence 12.8 and 32.2, and no others in the given range [Or greater accuracy 12.764..., 32.235...]

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Oct/Nov 2025 Paper 2 Variant 1, question 4.

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