∵2sin^2(C/2)=1--cosC.
cosC-1)=-2sin^2(C/2).
cosA+cosB=2cos(A+B)/2*cos(A-B)/2.
A+B=180-C.
(A+B)/2=90-C/2.
cos(A+B)/2=cos(90-C/2)=sin(C/2)
cosA+cosB+cosC-1=2sin(C/2)*cos(A-B)/2-2sin^2(C/2).
=2sin(C/2)[cos(A-B)-sin(C/2)].
=2sin(C/2)[cos(A-B)/2-coa(A+B)/2].
=2sin(C/2){-2sin[(A-B+A+B)/2][sin(A-B-A-B)/2].
=2sin(C/2)*[-2sinA*sin(-B)]
∴原式=4sin(C/2)sinA*SINB.