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A-LevelMathematicsTrigonometry9709/12 · May/June 2019 · Q45 Marks

Angle x is such that sinx = a + b and cos x = a – b, where a and b are constants.

  1. (i)Show that a² + b² has a constant value for all values of x.[3]
  2. (ii)In the case where tanx = 2, express a in terms of b.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

  1. [B1] a² + 2ab+b², a² – 2ab+b²
  2. [M1] Appropriate use of sin²x + cos²x = 1 with (a+b)² and (a−b)²
  3. [A1] a² + b² = 1/2
  4. [B1] 2a = (s+c) & 2b = (s−c) or a = 1/2(s+c) & b = 1/2(s-c)
  5. [M1] Appropriate use of sin²x + cos²x = 1
  6. [A1] a² + b² = 1/2
  7. [M1] Use of tanx = sinx/cosx to form an equation in a and b only
  8. [A1] a = 3b

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source
A-Level Mathematics, May/June 2019 Paper 1 Variant 2, question 4.

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