(A+B)/2+ C/2=90°, Sin(A+B)/2=cos C/2,cos(A+B)/2= Sin C/2, tan[(A+B)/2]= Sin(A+B)/2 /cos(A+B)/2= cos C/2 /Sin C/2, tan[(A+B)/2]=sinC可化为: cos C/2 /Sin C/2=2 Sin C/2 cos C/2 cos C/2=2 Sin ²C/2 cos C/2 cos C/2(1-2 Sin ²C/2)=0, cos C/2 cos C=0, cos C=0,C=90°. A+B=90°. sinA+sinB= sinA+cosA =√2sin(A+45°) 45°