If $x= \sec \theta -\cos \theta $ and $y=\sec^n \theta -\cos ^n \theta$ then $\bigg(\large\frac{dy}{dx}\bigg)^2=$

Question

$(a)\;\frac{n^2(y^2+2)}{x^2+4} \\ (b)\;\frac{(n^2+2)(y^2+4)}{(x^2+4)} \\ (c)\;\frac{x^2+4}{(y^2+4)} (n^2+2) \\ (d)\;\frac{y^2+4}{x^2+4}(n^2) $