C=60°,A+B=120°,c=3,a+b=5,
cosC=(a²+b²-c²)/(2ab)=1/2,
整理,得
3ab+9=(a+b)²=25,
得ab=16/3,
∴
cosA+cosB
=(b²+c²-a²)/(2bc)+(a²+c²-b²)/(2ac)
=[ab(a+b)+c²(a+b)-(a+b)(a²-ab+b²)]/(2abc)
=5/6,
∵cos[(A+B)/2]cos[(A-B)/2]
=(1/2)[cosA+cosB]
=5/12,
而cos[(A+B)/2]
=cos60°
=1/2,
∴cos[(A-B)/2]=5/6,