ITA 2011 — Questão 28

a) Calcule $\left(\cos^2 \dfrac{\pi}{5} - \operatorname{sen}^2 \dfrac{\pi}{5}\right) \cos \dfrac{\pi}{10} - 2 \operatorname{sen} \dfrac{\pi}{5} \cos \dfrac{\pi}{5} \operatorname{sen} \dfrac{\pi}{10}$.

b) Usando o resultado do item anterior, calcule $\operatorname{sen} \dfrac{\pi}{10} \cos \dfrac{\pi}{5}$.