SSC CGL 2023 PYQ — Question 71

The correct answer is option 2 i.e. 1.45.

Given that

If $\frac{sinx-cosx}{sinx+cosx}=\frac{2}{5}$,

Caculation

⇒ $\frac{sinx(1-cotx)}{sinx(1+cotx)}=\frac{2}{5}$

⇒ $\frac{(1-cotx)}{(1+cotx)}=\frac{2}{5}$

⇒ 5 - 5 cotx = 2 + 2 cotx

⇒ 7 cotx = 3

⇒ cotx = 3/7

Hence, the value $\frac{1+cot^2x}{1-cot^2x}$ = $\frac{1+9/49}{1-9/49}$ = 58/40 = 1.45