在三角形ABC中,若b/（cosA/2)=b/(cosB/2)=c/(cosC/2),则三角形ABC

网友回答

用正弦定理：sinA/a = sinB/b = sinC/c
因为：a/(cosA/2) = b/(cosB/2) = c/(cosc/2)
所以：sinA/(cosA/2) = sinB/(cosB/2) = sinC/(cosc/2)
再利用倍角公式：
2*sin(A/2)*cos(A/2)/(cosA/2) = 2*sin(B/2)*cos(B/2)/(cosB/2) = 2*sin(C/2)*cos(C/2)/(cosc/2)
所以：sin(A/2) = sin(B/2) = sin(C/2)
由于 0 所以：A = B = C
所以是等边三角形
注：pi是圆周率