Edexcel C2 — Question 4 9 marks

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Marks9
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicAddition & Double Angle Formulae
TypeProduct to sum using compound angles
DifficultyModerate -0.3 Part (a) is straightforward bookwork requiring recall of standard formulae and a guided algebraic manipulation with substitutions provided. Part (b) applies the result but requires recognizing that sin 4θ + sin 2θ = 0 leads to a product form, then solving multiple cases. While multi-step, the question provides significant scaffolding and uses standard C2 techniques throughout.
Spec1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals

  1. Write down formulae for sin (A + B) and sin (A - B). Using X = A + B and Y = A - B, prove that $$\sin X + \sin Y = 2 \sin \frac{X + Y}{2} \cos \frac{X - Y}{2}.$$ [4 marks]
  2. Hence, or otherwise, solve, for 0 ≤ θ < 360, $$\sin 40° + \sin 20° = 0.$$ [5 marks]

Question 4:
4
Question 4:
4
(a) Write down formulae for sin (A + B) and sin (A - B).

Using X = A + B and Y = A - B, prove that
$$\sin X + \sin Y = 2 \sin \frac{X + Y}{2} \cos \frac{X - Y}{2}.$$ [4 marks]

(b) Hence, or otherwise, solve, for 0 ≤ θ < 360,
$$\sin 40° + \sin 20° = 0.$$ [5 marks]

\hfill \mbox{\textit{Edexcel C2  Q4 [9]}}