If sinA = 8/17 and cosB = 12/13, where A and B are both acute, then cos(A − B) equals:

The 8-15-17 and 5-12-13 triangles give cosA = 15/17 and sinB = 5/13. Then cos(A − B) = cosA·cosB + sinA·sinB = 180/221 + 40/221 = 220/221 ≈ 0.995 — correctly close to 1, since A ≈ 28.1° and B ≈ 22.6° are only about 5.5° apart. Subtracting instead of adding gives cos(A + B) = 140/221; the remaining choices are sin(A + B) = 171/221 and sin(A − B) = 21/221.