△ABC中角A,B,C所对的边分别为a,b,c.已知asin²B/2+bsin²A/2=c/2

问题描述:

△ABC中角A,B,C所对的边分别为a,b,c.已知asin²B/2+bsin²A/2=c/2
(1)求证a,b,c成等差数列.
(2)若a-b=4,△ABC三个内角的最大角为120°,求△ABC的面积S

(1)∵asin²B/2+bsin²A/2=c/2∴a(1-cosB)+b(1-cosA)=ca-(a²+c²-b²)/2c+b-(b²+c²-a²)/2c=c2ac-a²-c²+b²+2bc-b²-c²+a²=2c²2ac+2bc=4c...