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WMA12/01 Oct 2020, Question 7: Harder Trig Equations

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 7 marks

The question, in short

Prove a trigonometric identity involving tan θ and 1/tan θ, then solve an equation in cos²(2x + 10°) for 0 ≤ x < 90°, giving answers to one decimal place.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (i) · 3 marks

Show that tan θ + 1/tan θ is equivalent to 1/(sin θ cos θ), stating the restriction θ ≠ nπ/2 for integer n.

  1. 1tan θ + 1/tan θ = sin θ/cos θ + cos θ/sin θ
  2. 2= (sin²θ + cos²θ)/(sin θ cos θ)
  3. 3= 1/(sin θ cos θ), since sin²θ + cos²θ = 1

AnswerShown: tan θ + 1/tan θ = (sin²θ + cos²θ)/(sin θ cos θ) = 1/(sin θ cos θ)

Part (ii) · 4 marks

Solve 3cos²(2x + 10°) = 1 for 0 ≤ x < 90°, giving answers in degrees to one decimal place, without graphical or numerical methods.

  1. 1cos²(2x + 10°) = 1/3, so cos(2x + 10°) = ±1/√3
  2. 2For 10° ≤ 2x + 10° < 190°: 2x + 10° = 54.74° or 125.26°
  3. 32x = 44.74° or 115.26°
  4. 4x = 22.4° or 57.6°

Answerx = 22.4°, 57.6°

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Also searched as: WMA12 October 2020 · WMA12/01 · wma12 oct20 · IAS Maths Pure Mathematics 2 October 2020 · question 7.
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