在△ABC中,三个内角A,B,C所对的边分别为a,b,c,向量m=(sinA,sinB-sinC)与n=(sinC-sinA,sinB+sinC)垂直
问题描述:
在△ABC中,三个内角A,B,C所对的边分别为a,b,c,向量m=(sinA,sinB-sinC)与n=(sinC-sinA,sinB+sinC)垂直
(1)求角B的大小
(2)若b=ccosA,△ABC的外接圆的面积为4π,求△ABC的面积
答
(1)m*n=0sinA(sinC-sinA)+(sinB-sinC)(sinB+sinC)=0sinAsinC-sin²A+sin²B-sin²C=0正玄定理代换ac-a²+b²-c²=0ac=a²+c²-b²cosB=(a²+c²-b²)/2ac=1/2...