If \(p\) and \(q\) are the length of the perpendiculars from the origin on the lines \(x \operatorname{cosec} \alpha-y \…

If \(p\) and \(q\) are the length of the perpendiculars from the origin on the lines \(x \operatorname{cosec} \alpha-y \sec \alpha=k \cot 2 \alpha\) and \(x \sin \alpha+y \cos \alpha=k \sin 2 \alpha\) respectively, then \(k^2\) is equal to?

[JEE Main 2021, 31 Aug (Shift 1)]