If sin θ - cos θ = $\frac{1}{29}$ find the value of sin θ + cos θ.

$\frac{41}{29}$

sinθ - cosθ =  \(\frac{1  }{29}\)

Concept used :-

If (a)sinθ - (b)cosθ =  c

then  (a)sinθ + (b)cosθ =  d

Hence,  a² + b² = c² + d²

a = 1 , b = 1 & c = \(\frac{1  }{29}\)

1² + 1² = ( \(\frac{1  }{29}\))² + d²

2 = \(\frac{1  }{841}\) + d²

 d² = \(\frac{1681  }{841}\)

d =  \(\frac{41  }{29}\)