If sinθ + cosθ = \(\frac{17}{13}\); and 0<θ<90°, then value of (sinθ - cosθ) is?

\(\frac{7}{13}\)

sinθ + cosθ = \(\frac{17}{13}\)         --- (i)

Now, let sinθ - cosθ = x     -----(ii)

squaring and adding eqn (i), (ii)

2(sin²θ + cos²θ) = \(\frac{289}{169}\) + x²

⇒ x² = 2 - \(\frac{289}{169}\) = \(\frac{338 - 289}{169}\)

⇒ x² = \(\frac{49}{169}\) ⇒ x = \(\frac{7}{13}\)