SSC CHSL 2023 PYQ — Question 54

The correct answer is option 1 i.e.  $\frac{1}{41}$

If sin θ + cos θ = $\frac{1}{29}$ 

a sin θ + b cos θ = c

a sin θ - b cos θ = d

then the value of a² + b² = c² + d²

sin θ + cos θ = $\frac{1}{29}$ 

sin θ - cos θ = d

Where, a = 1, b = 1 and c = 1/29

So,  1 + 1 = 1/841 + d²

d² = 2 - 1/841 

d = 41/29

Hence, $\frac{sinθ + cosθ}{sin θ - cos θ}$= (1/29)/(41/29) = $\frac{1}{41}$