If sinθ - cosθ = \(\frac{31}{41}\), find the value of sinθ + cosθ

\(\frac{7}{40}\) \(\frac{9}{41}\) \(\frac{41}{49}\) \(\frac{49}{41}\)

\(\frac{49}{41}\)

⇒ sinθ - cosθ = \(\frac{31}{41}\) ⇒ \(\frac{P}{H}\) - \(\frac{B}{H}\) = \(\frac{31}{41}\) ⇒ \(\frac{P - B}{H}\) = \(\frac{31}{41}\) Use triplets, (9, 40, 41) P = 40, B = 9, H = 41 ⇒ sinθ + cosθ = \(\frac{P}{H}\) + \(\frac{B}{H}\) = \(\frac{40}{41}\) + \(\frac{9}{41}\) = \(\frac{49}{41}\)