已知△ABC的内角A B C的对边为a b c 且a/b=(1+cosA)/cosC 求角A

问题描述:

已知△ABC的内角A B C的对边为a b c 且a/b=(1+cosA)/cosC 求角A

a/b=(1+cosA)/cosC sinA/sinB=(1+cosA)/cosC sinAcosC =sinB+sinBcosAsinAcosC=sin(A+C)+sinBcosAsinAcosC=sinAcosC+cosAsinC+sinBcosAcosA(sinC+sinB)=0sinC+sinB不等于0cosA=0A=90度△ABC是直角三角形