We know sin(a) & cos(b), but we don't know cos(a) or sin(b). Or do we?
We can figure it out by drawing two right triangles. On the first triangle, label one of the acute angles as "a." sine is defined as opposite/hypotenuse, so label the opposite side 3 and the hypotenuse 5. Use the Pythagorean theorem to find the missing side (adjacent). Then find cos(b) (adjacent over hypotenuse).
Do it again with another triangle. Label one of the acute angles as "b." cos(b) = 9/41, so the adjacent side is 9 and the hypotenuse is 41. Use the Pythagorean theorem again to find the missing side (opposite). Now find sin(b).
Finally, plug in all the ratios into the identity I wrote above and evaluate.