△ABC中A+B=2π/3,则cos²A+cos²B+cosC的取值范围是

△ABC中A+B=2π/3,则cos²A+cos²B+cosC的取值范围是
△ABC中A+B=2π/3,则cos²A+cos²B+cosC的取值范围是

△ABC中A+B=2π/3,则cos²A+cos²B+cosC的取值范围是
cosc=-cos(A+B)=1/2
Cos^2A+cos^2B+1/2
=(1+cos2A+1+cos2B)/2+1/2
=1-cos(A+B)cos(A-B)
=1-cos(A-B)/2
A-B=t
A+B=2TT/3
t=2TT/3-2B 2TT/3>B>0 -4TT/3