Question

sin (x-y) if cos x = 8/17 and cos y = 3/5

Answer 1

Using a trig identity, we can define tan(x - y) as:

(tanx - tany)/(1 + tanxtany)

If sinx is 8/17, that means tanx = 8/15 (Draw a triangle and use the SOHCAHTOA rules)
Likewise, if cosy is 3/5, then tany = 4/3

Just plug in those values into the formula above to get your answer.
The answer ends up being -36/77