Final answer:
To simplify the expression sin(x-y) - sin(xy), use the trigonometric identity sin(a - b) = sin(a)cos(b) - cos(a)sin(b).
Step-by-step explanation:
To simplify the expression sin(x-y) - sin(xy), we can start by using the trigonometric identity sin(a - b) = sin(a)cos(b) - cos(a)sin(b). Applying this identity, we have:
sin(x-y) - sin(xy) = sin(x)cos(y) - cos(x)sin(y) - sin(x)sin(y)x - cos(x)cos(y)x
Next, we can factor out the common terms:
sin(x)cos(y) - sin(x)sin(y)x - cos(x)sin(y) - cos(x)cos(y)x
Finally, we can combine like terms to simplify further. This gives us the simplified expression: sin(x)[cos(y) - sin(y)x] - cos(x)[sin(y) + cos(y)x].