Vous avez : tan(x)=(racine carré de 3)/4=1,732/4=0,433 ,
de plus vous avez : 2sin(x)+cos(x) = cos(x)*(2tan(x)+1) et sin(x)-cos(x)=cos(x)*(tan(x)-1) , donc: (2sin(x)+cos(x))/(sin(x)-cos(x)) = (2tan(x)+1)/(tan(x)-1) =(2*0,433+1)/(0,433-1)=1,866/(-0,567)=-1,866/0,567=-3,29 .
Exercice III :
On a :
E = (tan(45°)-tan(60°))/(1+tan(45°)tan(60°)) = (1-1,732)/(1+1,732) =(-0,732)/2,732=-0,268
ou bien on a : tan(a-b)=(tan(a)-tan(b))/(1+tan(a)tan(b)) , en posant a=45° et b=60° on a : E=(tan(45°)-tan(60°))/(1+tan(45°)tan(60°))=tan(45°-60°)=tan(-15°)=-tan(15°)=-0,268 .
Lista de comentários
Exercice I :
Vous avez : tan(x)=(racine carré de 3)/4=1,732/4=0,433 ,
de plus vous avez :
2sin(x)+cos(x) = cos(x)*(2tan(x)+1) et sin(x)-cos(x)=cos(x)*(tan(x)-1) ,
donc:
(2sin(x)+cos(x))/(sin(x)-cos(x)) = (2tan(x)+1)/(tan(x)-1)
=(2*0,433+1)/(0,433-1)=1,866/(-0,567)=-1,866/0,567=-3,29 .
Exercice III :
On a :
E = (tan(45°)-tan(60°))/(1+tan(45°)tan(60°)) = (1-1,732)/(1+1,732)
=(-0,732)/2,732=-0,268
ou bien on a : tan(a-b)=(tan(a)-tan(b))/(1+tan(a)tan(b)) ,
en posant a=45° et b=60° on a :
E=(tan(45°)-tan(60°))/(1+tan(45°)tan(60°))=tan(45°-60°)=tan(-15°)=-tan(15°)=-0,268 .