If \(p\) and \(q\) are the length of the perpendiculars from the origin on the lines \(\text{xcosec}\alpha - ysec\alpha …

If \(p\) and \(q\) are the length of the perpendiculars from the origin on the lines \(\text{xcosec}\alpha - ysec\alpha = k\ cot2\alpha\) and \(\text{xsin}\alpha + ycos\alpha = ksin2\alpha\) respectively, then \(k^{2}\) is equal to?

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