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A-LevelMathematicsTrigonometry9709/31 · Oct/Nov 2022 · Q45 Marks

Solve the equation tan(x + 45°) = 2 cotx for 0° < x < 180°.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

  1. [M1] Use correct tan(A + B) formula and obtain an equation in tan x or an equation in cos x and sin x
  2. [A1] Obtain correct 3 term equation tan²x + 3tan x - 2 = 0, or equivalent
  3. [M1] Solve a 3-term quadratic in tan x and obtain a value for x
  4. [A1] Obtain answer, e.g. 29.3°
  5. [A1] Obtain second answer, e.g. 105.7° and no other

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Oct/Nov 2022 Paper 3 Variant 1, question 4.

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