A2 June 2022 Paper 1 Q2

2 Simplify

\[\frac{\cos\left(\dfrac{6\pi}{13}\right) + \mathrm{i}\sin\left(\dfrac{6\pi}{13}\right)}{\cos\left(\dfrac{2\pi}{13}\right) - \mathrm{i}\sin\left(\dfrac{2\pi}{13}\right)}\]

Tick (✓) one box. [1 mark]

• \(\cos\left(\dfrac{8\pi}{13}\right) + \mathrm{i}\sin\left(\dfrac{8\pi}{13}\right)\)
• \(\cos\left(\dfrac{8\pi}{13}\right) - \mathrm{i}\sin\left(\dfrac{8\pi}{13}\right)\)
• \(\cos\left(\dfrac{4\pi}{13}\right) + \mathrm{i}\sin\left(\dfrac{4\pi}{13}\right)\)
• \(\cos\left(\dfrac{4\pi}{13}\right) - \mathrm{i}\sin\left(\dfrac{4\pi}{13}\right)\)