化简：sin(α-β)sin(β-r)-cos(α-β)cos(r-β)

网友回答

使用积化和差:
sin(α-β)sin(β-r)-cos(α-β)cos(r-β)
=(-1/2)[cos(α-β+β-r)-cos(α-β-β+r)]-(1/2)[cos(α-β+r-β)+cos(α-β-r+β)]
=(-1/2)[cos(α-r)-cos(α+r-2β)]-(1/2)[cos(α+r-2β)+cos(α-r)]
=-cos(α-r)