Question

在△abc中,若sina sinb=cos2(c/2)

在△ABC中,若sinAsinB=cos2（C/2）,则下面等式一定成立的是
A.A=B
B.A=C
C.B=C
D.C=90°
答案是选A,求详细解题步骤^ ^

Answer 1

根据cosC=2cos^2(C/2)-1sinAsinB=0.5*(cosC+1)sinAsinB=0.5cos(pi-A-B)+0.5sinAsinB=-0.5cos(A+B)+0.5sinAsinB=-0.5cosAcosB+0.5sinAsinB+0.5sinAsinB+cosAcosB=1cos(A-B)=1A=B选A