Cos(x-y+(пи/2))+2sin(x+пи)cos(y-пи) . Упростите выражение

[latex]cos(x-y+ \frac{ \pi }{2} )=-sin(x-y) \\ \\ 2sin(x+ \pi )cos(y- \pi )= 2sin( \pi +x)cos( \pi-y )= \\ \\ =2\cdot(-sinx)\cdot (-cosy) =2sinx\cdot cosy[/latex] [latex]cos(x-y+ \frac{ \pi }{2} )+2sin(x+ \pi )cos(y- \pi )=-sin(x-y)+2sinx\cdot cosy= \\ \\ = -(sinx\cdot cosy-cosx\cdot siny)+2sinx\cdot cosy= \\ \\=-sinx\cdot cosy+cosx\cdot siny+2sinx\cdot cosy= \\ \\ =sinx\cdot cosy+cosx\cdot siny=sin(x+y)[/latex]