If sinθ + cosθ = \(\frac{7}{13}\), then find value of sinθ - cosθ?

\(\frac{10}{26}\) \(\frac{17}{13}\) \(\frac{32}{72}\) \(\frac{65}{144}\)

\(\frac{17}{13}\)

sinθ + cosθ = \(\frac{7}{13}\)         --- (i) Now, let sinθ - cosθ = x     -----(ii) squaring and adding eqn (i), (ii) 2(sin2θ + cos2θ) = \(\frac{49}{169}\) + x2 ⇒ x2 = 2 - \(\frac{49}{169}\) = \(\frac{338\;-\;49}{169}\) ⇒ x2 = \(\frac{289}{169}\) ⇒ x = \(\frac{17}{13}\)