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A-LevelMathematicsTrigonometry9709/32 · Feb/Mar 2021 · Q36 Marks

By first expressing the equation tan(x + 45°) = 2 cotx + 1 as a quadratic equation in tanx, solve the equation for 0° < x < 180°.

  1. By first expressing the equation tan(x + 45°) = 2 cotx + 1 as a quadratic equation in tanx, solve the equation for 0° < x < 180°.[6]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2021). The mark or mark type is shown in brackets.

  1. [*M1] Use correct trig formulae to obtain an equation in tan x
  2. [DM1] Using tan 45° = 1, obtain a horizontal equation in tan x in any form
  3. [A1] Reduce the equation to tan²x+tanx-1=0, or 3-term equivalent
  4. [M1] Solve a 3-term quadratic in tan x, for x
  5. [A1] Obtain answer, e.g. x = 31.7°
  6. [A1] Obtain second answer, e.g. x = 121.7°, and no other in the interval

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Feb/Mar 2021 Paper 3 Variant 2, question 3.

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