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

\(\frac{17}{12}\) \(\frac{7}{13}\) \(\frac{13}{17}\) \(\frac{17}{13}\)

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

⇒ sinθ - cosθ = \(\frac{7}{13}\) ⇒ \(\frac{P}{H}\) - \(\frac{B}{H}\) = \(\frac{7}{13}\) ⇒ \(\frac{P - B}{H}\) = \(\frac{7}{13}\) Use triplets, (5, 12, 13) P = 12, B = 5, H = 13 ⇒ sinθ + cosθ = \(\frac{P}{H}\) + \(\frac{B}{H}\) = \(\frac{12}{13}\) + \(\frac{5}{13}\) = \(\frac{17}{13}\)