Réponses

  • Utilisateur Brainly
2013-04-23T10:12:33+02:00

(tan(90°-2α)-tan(90°-3α)) / (tan(90°-α)-tan(90°-2α)) = 20/55

 

tan(a)-tan(b)=tan(a-b)[1+tan(a).tan(b)]

et tan(90°-β=1/tan(β)

 

donc tan(90°-3α)=1/tan(3α)

          tan(90°-2α)=1/tan(2α)

          tan(90°-2α)=1/tan(2α)

 

donc (tan(90°-2α)-tan(90°-3α)) / (tan(90°-α)-tan(90°-2α)) = 20/55 donne :

(1/tan(2α)-1/tan(3α))/(1/tan(α)-1/tan(2α))=20/55

 

on trouve alors (après plusieurs lignes de calculs ...) α=14,47°