由正弦定理及等比定理得：
a/sinA=b/sin B=c/sinC=(a+b)/( sinA+ sin B)
将c=3,C=60°,a+b=5代入得：3/sin60°=5/( sinA+ sin B)
sinA+ sin B=5√3/6.
2sin((A+B)/2)cos((A-B)/2) =5√3/6.
2×sin60°cos((A-B)/2) =5√3/6.
∴cos((A-B)/2) =5/6.