cos2A-cos2B=2sin²C,试判断三角形ABC的形状

cos2A-cos2B=2sin²C,试判断三角形ABC的形状
cos2A-cos2B=2sin²C,试判断三角形ABC的形状

cos2A-cos2B=2sin²C,试判断三角形ABC的形状
cos2A-cos2B=2sin²C
1-2sin^2A-(1-2sin^2B)=2sin^2C
sin^2B=sin^2A+sin^2C
用正弦定理a/sinA=b/sinB=c/sinC
很容易得到
b^2=a^2+c^2
因此是以B为直角的直角三角形