In a right triangle the hypotenuse measures 41 cm and the shorter leg 9 cm. For the acute angle θ facing the 9 cm side, cosθ − sinθ equals:

The remaining side is √(1681 − 81) = √1600 = 40 cm, so sinθ = 9/41 and cosθ = 40/41 and the difference is 31/41 ≈ 0.756. The sum of the same two ratios is 49/41; the negative −31/41 comes from subtracting the wrong way round, which cannot happen here because θ faces the shorter leg and so has the smaller sine; and 9/40 is tanθ.