△ABC的三内角A,B,C的对边分别是a,b,c,且a,b,c成等比数列,cosA,cosB,cosC成等差数列,则△ABC为.要过

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△ABC的三内角A,B,C的对边分别是a,b,c,且a,b,c成等比数列,cosA,cosB,cosC成等差数列,则△ABC为.要过

只能是等边!先用余弦定理:sin^2B=sin^2A+sin^2C-2sinAsinCcosBsin^2B=sinAsinC,cosB=(cosA+cosC)/2代入上式并移项:sin^2A+sin^2C=sinAsinC(1+cosA+cosC)大于等于2sinAsinC因此cosA+cosC>=1,cosB>=1/2.下面用反证法...