If sin2θ = 24/25, then $(sin\theta +cos\theta {)}^2$ equals:

$(sin\theta +cos\theta {)}^2=si$$n^2$θ + $co$$s^2$θ + 2sinθ·cosθ = 1 + sin2θ = 1 + 24/25 = 49/25. No quadrant information is needed, because only the square is asked for. The companion $(sin\theta -cos\theta {)}^2=1-$ sin2θ = 1/25 is the sign trap, 7/5 is the square root — the answer to a question that was not asked — and 24/25 forgets the 1.