Question

sinx+siny+sin(x+y)=4sinx/2cosx/2cosx-y/2

Answer 1

sinx+siny+sin(x-y)=4sin(x/2)cos(x/2)cos((x-y)/2);

sinx+siny+sin(x-y)=2sin((x+y)/2)·cos((x-y)/2)+2sin(x-y)/2·cos(x-y)/2=

=2cos((x-y)/2)·[sin(x+y)/2+sin(x-y)/2)]=

=2cos((x-y)/2)·2sin((x+y+x-y)/4)·cos((x+y-x+y)/4)=

=4cos((x-y)/2)·sin(x/2)·cos(y/2)