三角形ABC三内角ABC依次成等差数列,则sinA的平方+sinC的平方的取值范围是什么?

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三角形ABC三内角ABC依次成等差数列
则有 A=60-X,B=60 C=60+X X>=0所以(SINA)^2+(SINC)^2=(SIN(60-X))^2+(SIN(60+X))^2
=(SIN60*COSX-COS60*SINX)^2+(SIN60*COSX+COS60*SINX)^2
=2*(3/2)*(COSX)^2+2*(1/2)*(SINX)^2
=3(COSX)^2+(SINX)^2=2(COSX)^2+1
因为 -1