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A-LevelMathematicsTrigonometry9709/12 · Oct/Nov 2014 · Q56 Marks

Show that the equation 1 + sin x tan x = 5 cos x can be expressed as 6 cos²x - cos x − 1 = 0.

  1. (i)Show that the equation 1 + sin x tan x = 5 cos x can be expressed as 6 cos²x - cos x − 1 = 0.[3]
  2. (ii)Hence solve the equation 1 + sin x tan x = 5 cos x for 0° ≤ x ≤ 180°.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2014). The mark or mark type is shown in brackets.

  1. [1] Replaces tan x by sin x / cos x. Correct formula
  2. [1] Replaces sin²x by 1 - cos²x. Correct formula used in appropriate place
  3. [1] → 6cos²x - cos x - 1 (= 0). AG
  4. [1] Soln of quadratic → (cos x = -⅓ or ½). Correct method
  5. [2] → x = 60° or 109.5°. co co

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.
Source
A-Level Mathematics, Oct/Nov 2014 Paper 1 Variant 2, question 5.

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