在三角形ABC中,abc成等差数列,
根据正弦定理转换,那么sinA,sinB ,sinC也是等差数列
则2sinB = sinA + sinC
B = 180 - A - C
2sinB = 2sin(180-A-C) = 2sin(A+C) = sinA + sinC
sinA + sinC = 2 * sin[(A+C)/2] * cos[(A-C)/2]
2sin(A+C) = 4 * sin[(A+C)/2] * cos[(A+C)/2]
所以2(cos(A+C)/2)=cos((A-C)/2)