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O-LevelAdditional MathematicsTrigonometry4037/21 · Oct/Nov 2011 · Q77 Marks

Given that tan x = p, find an expression, in terms of p, for cosec²x.

  1. (a)Given that tan x = p, find an expression, in terms of p, for cosec²x.[3]
  2. (b)Prove that (1 + secθ)(1 – cosθ) = sinθ tanθ.[4]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2011). The mark or mark type is shown in brackets.

  1. [1] cot² x = 1/tan² x
  2. [1] cosec²x = 1 + cot²x
  3. [1] = 1 + 1/p² or (p²+1)/p²
  4. [1] OR Draw triangle with 1, p and √(p²+1) correct
  5. [1] cosec x = √(p²+1)/p
  6. [1] cosec²x = (p²+1)/p²
  7. [1] secθ = 1/cosθ
  8. [1] Multiply out and correct use Pythagoras
  9. [1] (sin²θ/cosθ)
  10. [1] sinθ tanθ

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About this question

Topic
Trigonometry, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2011 Paper 2 Variant 1, question 7.

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