已知锐角abc满足sina-sinb+siny=0,cosa-cosb-cosy=0,求a-b

已知锐角abc满足sina-sinb+siny=0,cosa-cosb-cosy=0,求a-b
已知锐角abc满足sina-sinb+siny=0,cosa-cosb-cosy=0,求a-b

已知锐角abc满足sina-sinb+siny=0,cosa-cosb-cosy=0,求a-b
sina-sinb+siny=0,
cosa-cosb-cosy=0
siny=sinb-sina
cosy=cosa+cosb
分别平方,相加
sin²y+cos²y=sin²a+cos²a+sin²b+cos²b-2(cosacosb+sinasinb)
1=1+1-2cos(a-b)
cos(a-b)=1/2
0

sina-sinb+siny=0=>siny=sinb-sina 1)
cosa-cosb-cosy=0=>cosy=cosa-cosb 2)
1)^2+2)^2,
1=2-2sinasinb-2cosacosb
sinasinb+cosacosb=1/2
cos(a-b)=1/2
a-b=±60°