设a=(x+y)/2 ,b=(x–y)/2
那么 x=a+b ,y=a–b
所以
sinx–siny=sin(a+b)–sin(a–b)
=sina*cosb+cosa*sinb– (sina*cosb–cosa*sinb)
= sina*cosb+cosa*sinb–sina*cosb+cosa*sinb
=2 cosa*sinb
=2sin(x–y)/2*cos(x+y)/2