△ABC中A+B=2π/3,则cos²A+cos²B+cosC的取值范围是
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![△ABC中A+B=2π/3,则cos²A+cos²B+cosC的取值范围是](/uploads/image/z/5504473-1-3.jpg?t=%E2%96%B3ABC%E4%B8%ADA%2BB%3D2%CF%80%2F3%2C%E5%88%99cos%26%23178%3BA%2Bcos%26%23178%3BB%2BcosC%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E6%98%AF)
△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