三角形abc中,角a、b、c满足2sinb=sina+sinc.求证:cos(a-c)=2cos(a+c)

2sinB=2sin(pi-A-C)=2sin(A+C)=sinA+sinC=2sin((A+C)/2)cos((A-C)/2)所以4sin((A+C)/2)cos((A+C)/2)=2sin((A+C)/2)cos((A-C)/2)所以2cos((A+C)/2)=cos((A-C)/2)展开得到2cosA/2cosC/2-2sinA/2sinC/2=cosA/2cosC/2+si...