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A-LevelMathematicsTrigonometry9709/32 · Oct/Nov 2024 · Q23 Marks

By sketching a suitable pair of graphs, show that the equation cot2x = secx has exactly one root in the interval 0 < x < ½π.

  1. (a)By sketching a suitable pair of graphs, show that the equation cot2x = secx has exactly one root in the interval 0 < x < ½π.[2]
  2. (b)Show that if a sequence of real values given by the iterative formula xn+1 = ½ tan⁻¹(cosx) converges, then it converges to the root in part (a).[1]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

  1. [B1] Sketch a relevant graph, e.g. y = cot 2x
  2. [B1] Sketch a second relevant graph on the same axes, e.g. y = sec x and justify the given statement
  3. [B1] State x = ½ tan⁻¹(cosx) and rearrange to the given equation cot 2x = sec x

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About this question

Topic
Trigonometry, A-Level Mathematics (syllabus 9709). Structured question, 3 marks.
Source
A-Level Mathematics, Oct/Nov 2024 Paper 3 Variant 2, question 2.

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