Выражение : sin(a+b)*cos(a+b)+sin(a-b)*cos(a-b)=?

1/2(sin(a+b-a-b)+sin(a+b+a+b)) +1/2(sin(a-b-a+b)+sin(a-b+a-b))=
=1/2(sin0+sin(2s+2b)) +1/2(sin0+sin(2a-2b)=1/2sin(2a+2b)+1/2(sin(2a-2b)=
=1/2*1/2(cos(2a+2b-2a+2b)-cos(2a+2b+2a-2b)=1/4(cos4b-cos4a)=
=-1/2sin(2b+2a)sin(2b-2a)