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O-LevelAdditional MathematicsTrigonometry4037/12 · Oct/Nov 2012 · Q36 Marks

Show that cotθ + sinθ / (1 + cosθ) = cosecθ.

  1. (i)Show that cotθ + sinθ / (1 + cosθ) = cosecθ.[5]
  2. (ii)Explain why the equation cotθ + sinθ / (1 + cosθ) = 1/2 has no solution.[1]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2012). The mark or mark type is shown in brackets.

  1. [B1] B1 for cotθ = cosθ/sinθ
  2. [M1] M1 for attempt to add fractions
  3. [M1] M1 for use of identity
  4. [M1] M1 for algebra/simplification
  5. [A1] Must see cosec θ for A1
  6. [B1] Gives cosec θ = 0.5, leads to sin θ = 2 which has no solutions. Needs an explanation

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About this question

Topic
Trigonometry, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2012 Paper 1 Variant 2, question 3.

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