If p and q are the lengths of the perpendiculars from the origin on the lines, x cosec α-y sec α= k cot 2 α and x sin α+y cos α= k sin 2 α…

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