SSC CGL 2023 PYQ — Question 59

The correct answer is option 1 i.e. tan$\theta$ 
$\frac{sin\theta- 2sin^3\theta}{ 2 cos^3\theta -cos\theta }$

⇒ $\frac{sinθ(1−2sin^2θ)}{cosθ(2cos^2θ−1)}$

the terms 1 − 2sin⁡²θ and 2cos⁡²θ − 1 are the same because of the Pythagorean identity:

⇒ sin⁡²θ + cos⁡²θ = 1

Thus, 1 − 2sin⁡²θ = 2cos⁡²θ − 1

So, sin⁡θ/cos⁡θ = tanθ