If sin θ - cos θ = 7/17, then find the value of sinθ + cos θ.

Concept used :-

If (a)sinθ - (b)cosθ =  c

then  (a)sinθ + (b)cosθ =  c

Hence,  a² + b² = c² + d²

sin θ - cos θ = \(\frac{7}{17}\)

a = 1 , b = 1 & c = \(\frac{7}{17}\)

1² + 1² = ( \(\frac{7}{17}\))² + d²

on solving,

d = \(\frac{23}{17}\)

So,

sinθ + cosθ = \(\frac{23}{17}\)