| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Addition & Double Angle Formulae |
| Type | Product to sum using compound angles |
| Difficulty | Moderate -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. |
| Spec | 1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals |
(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]}}