If sinθ + cosθ = 7/5 and sinθ > cosθ, then sinθ − cosθ equals:

Squaring the given equation: 1 + 2sinθ·cosθ = 49/25, so sinθ·cosθ = 12/25. Then $(sin\theta -cos\theta {)}^2=1-2(12/25)=1/25$, so the difference is ±1/5, and the condition sinθ > cosθ selects +1/5. (Indeed sinθ = 4/5 and cosθ = 3/5.) Forgetting to take the square root leaves 1/25.