If \(\mathrm{p}\) and \(\mathrm{q}\) are the lengths of the perpendiculars from the origin on the lines. \(x \operatorna…

If \(\mathrm{p}\) and \(\mathrm{q}\) are the lengths 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)]