sin(a+B)cosa-1/2[ sin(2a+B)-sinB]
=sin(a+B)cosa-1/2[ sin(a+B+a)-sinB]
=sin(a+B)cosa-(1/2)[sin(a+B)cosa+cos(a+B)sina-sinB]
=(1/2)[sin(a+B)cosa-cos(a+B)sina+sinB]
=(1/2)[sin(a+B-B)+sinB]=sinB
sin(a+B)cosa-1/2[ sin(2a+B)-sinB]
=sin(a+B)cosa-1/2[ sin(a+B+a)-sinB]
=sin(a+B)cosa-(1/2)[sin(a+B)cosa+cos(a+B)sina-sinB]
=(1/2)[sin(a+B)cosa-cos(a+B)sina+sinB]
=(1/2)[sin(a+B-B)+sinB]=sinB