The first point is that the two terms inside the sine are angles. To solve this I would apply the identity for the difference of two angles.
For our example we would apply the formula as if:
A = sin-1(9/41) and B=cos-1(-4/5)
The original expression can now be written as:
From here you will want to find each factor individually.
If we set A = sin-1(9/41), then:
sin[sin-1(9/41)] = sin(A)
sin[sin-1(9/41)] = 9/41
cos[cos-1(-4/5)] = -4/5
Now we need to find sin(B) and cos(A). Do you see how to do that? If you have sin(A)=9/41 there should be a certain identity that you can use to find the cos(A).