Sin(-180-x)

This is my attempt

First I used sum/difference formulae

Sin(A-B) =sinAcosB-cosAsinB

=sin(-180)cos(x)-cos(-180)sin(x)

=-sin(180)cos(x) - - cos(180)sin(x)

=0.cos(x) + (-1)]sin(x)

=-sin(x)

My another option was to multiply by (-1)

After multiply I have sin (180+x) which I knw Sin(x) is negative in third quadrant(not sure about this method though)

According to my textbook answer is Sin (x)

Where did I lost it??