△ABC的三个内角A,B,C所对的边分别为a,b,c,asinAsinB+bcos²A=2a,(1)求b/a,(2)求A的取值范围.
问题描述:
△ABC的三个内角A,B,C所对的边分别为a,b,c,asinAsinB+bcos²A=2a,(1)求b/a,(2)求A的取值范围.
答
∵a/sinA=b/sinB=c/sinC=2R∴a=2RsinA b=2RsinB c=2RsinC代入已知式子得,2Rsin²AsinB+2RsinBcos²A=4RsinA即2RsinB(sin²A+cos²A)=4RsinA即sinB=2sinA∴b/a=sinB/sinA=2∴0