Montrer que : [tex]cos(frac{pi}{20})+cos(frac{9pi}{20})=frac{1}{2}sqrt{3+sqrt{5}}[/tex]
Mathématiques
Abiola868
Question
Montrer que :
[tex]cos(frac{pi}{20})+cos(frac{9pi}{20})=frac{1}{2}sqrt{3+sqrt{5}}[/tex]
[tex]cos(frac{pi}{20})+cos(frac{9pi}{20})=frac{1}{2}sqrt{3+sqrt{5}}[/tex]
1 Réponse
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1. Réponse Anonyme
cos(π/20)+cos(9π/20)
=2*cos((π/20+9π/20)/2)*cos((π/20-9π/20)/2)
=2*cos(π/4)*cos(-π/5)
=2*(√2/2)*(1+√5)/4
=1/4*(√2+√10)