If sinθ + cosθ = 7/13 , then find value of sinθ - cosθ?

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 = \(\frac{17}{13}\)