If cotθ = 8/15 and θ is acute, then sinθ + cosθ equals:

cotθ = adjacent/opposite = 8/15 puts the sides at 8 and 15, so the hypotenuse is √(64 + 225) = 17. Then sinθ = 15/17, cosθ = 8/17 and the sum is 23/17 ≈ 1.35 — comfortably below the ceiling √2 ≈ 1.414. The value 7/17 is the difference, and 17/23 flips the fraction.