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4PM1/02 Nov 2021, Question 1: The Addition Formulae

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 5 marks

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The question, in short

Use the cos(A + B) formula to prove cos 2A = 1 − 2sin²A, then with sin A = (x + 1)/2 and cos 2A = (4 − y)/3 show that y = (1/2)(3x² + 6x + 5).

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Part (a) · 2 marks

Starting from the cos(A + B) identity, show that cos 2A equals 1 − 2sin²A.

  1. 1cos(A + A) = cos A cos A − sin A sin A, so cos 2A = cos²A − sin²A
  2. 2cos²A = 1 − sin²A
  3. 3cos 2A = 1 − sin²A − sin²A = 1 − 2sin²A

Answercos 2A = 1 − 2sin²A shown

Part (b) · 3 marks

Given sin A = (x + 1)/2 and cos 2A = (4 − y)/3, show that y = (1/2)(3x² + 6x + 5).

  1. 1(4 − y)/3 = 1 − 2((x + 1)/2)²
  2. 2(4 − y)/3 = 1 − (x² + 2x + 1)/2
  3. 34 − y = 3 − (3/2)(x² + 2x + 1)
  4. 4y = 1 + (3/2)(x² + 2x + 1) = (1/2)(3x² + 6x + 5)

Answery = (1/2)(3x² + 6x + 5) shown

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