For the next two (02) items that follow: 12(tanθ + cotθ) = 25, where 45° < θ < 90° What is the value of (sinθ - cosθ)?

tanθ + cotθ = sinθ/cosθ + cosθ/sinθ = (sin²θ + cos²θ)/(sinθ cosθ) = 1/(sinθ cosθ). So 12/(sinθ cosθ) = 25, giving sinθ cosθ = 12/25. Then (sinθ - cosθ)² = sin²θ + cos²θ - 2 sinθ cosθ = 1 - 24/25 = 1/25. So sinθ - cosθ = ±1/5. Since 45° < θ < 90°, sinθ > cosθ, so sinθ - cosθ > 0, giving 1/5.