两角和差公式sinx-siny=2sin[(x-y)/2]cos[(x+y)/2]推导.

sinx-siny
=sin[(x-y)/2 + (x+y)/2] -sin[(x+y)/2 -(x-y)/2] （变形后再利用两角和与差的正弦公式）
=sin[(x-y)/2]cos[(x+y)/2] +cos[(x-y)/2]sin[(x+y)/2] -{sin[(x+y)/2]cos[(x-y)/2] -cos[(x+y)/2]sin[(x-y)/2]}
=2sin[(x-y)/2]cos[(x+y)/2]