Répondre :
Bonsoir,
Appliquons la formule : [tex]cos(p)+cos(q)=2cos(\dfrac{p+q}{2})cos(\dfrac{p-q}{2})[/tex]
[tex]cos(\dfrac{4\pi}{5})+cos(\dfrac{6\pi}{5})=2cos(\dfrac{\dfrac{4\pi}{5}+\dfrac{6\pi}{5}}{2})cos(\dfrac{\dfrac{4\pi}{5}-\dfrac{6\pi}{5}}{2})\\\\cos(\dfrac{4\pi}{5})+cos(\dfrac{6\pi}{5})=2cos(\dfrac{2\pi}{2})cos(\dfrac{-\dfrac{2\pi}{5}}{2})\\\\cos(\dfrac{4\pi}{5})+cos(\dfrac{6\pi}{5})=2cos(\pi)cos(\dfrac{-\pi}{5})\\\\cos(\dfrac{4\pi}{5})+cos(\dfrac{6\pi}{5})=2\times(-1)cos(\dfrac{-\pi}{5})\\\\cos(\dfrac{4\pi}{5})+cos(\dfrac{6\pi}{5})=-2cos(\dfrac{\pi}{5})[/tex]
(Il faut se souvenir que deux angles opposés ont des cosinus égaux)
Appliquons la formule : [tex]cos(p)+cos(q)=2cos(\dfrac{p+q}{2})cos(\dfrac{p-q}{2})[/tex]
[tex]cos(\dfrac{4\pi}{5})+cos(\dfrac{6\pi}{5})=2cos(\dfrac{\dfrac{4\pi}{5}+\dfrac{6\pi}{5}}{2})cos(\dfrac{\dfrac{4\pi}{5}-\dfrac{6\pi}{5}}{2})\\\\cos(\dfrac{4\pi}{5})+cos(\dfrac{6\pi}{5})=2cos(\dfrac{2\pi}{2})cos(\dfrac{-\dfrac{2\pi}{5}}{2})\\\\cos(\dfrac{4\pi}{5})+cos(\dfrac{6\pi}{5})=2cos(\pi)cos(\dfrac{-\pi}{5})\\\\cos(\dfrac{4\pi}{5})+cos(\dfrac{6\pi}{5})=2\times(-1)cos(\dfrac{-\pi}{5})\\\\cos(\dfrac{4\pi}{5})+cos(\dfrac{6\pi}{5})=-2cos(\dfrac{\pi}{5})[/tex]
(Il faut se souvenir que deux angles opposés ont des cosinus égaux)