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A-LevelMathematicsTrigonometry9709/12 · Oct/Nov 2016 · Q25 Marks

Express the equation sin 2x + 3 cos 2x = 3(sin 2x – cos 2x) in the form tan 2x = k, where k is a constant.

  1. (i)Express the equation sin 2x + 3 cos 2x = 3(sin 2x – cos 2x) in the form tan 2x = k, where k is a constant.[2]
  2. (ii)Hence solve the equation for −90° ≤ x ≤ 90°.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.

  1. [M1] Expand and collect as far as tan2x = a constant from sin cos soi
  2. [A1] → tan2x = 3 or k =3 cwo
  3. [M1] Inverse then ÷2. soi.
  4. [A1 A1] on 1st answer +/ – 90° if in given range but no extra solutions in the given range.
  5. [SR A1A0] Both

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, Oct/Nov 2016 Paper 1 Variant 2, question 2.

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