$ VT = \dfrac{\sin^2\alpha - \cos^2\alpha + \cos^4\alpha}{\cos^2\alpha - \sin^2\alpha + \sin^4\alpha} \\ = \dfrac{1 - 2\cos^2\alpha + \cos^4\alpha}{1 - 2\sin^2\alpha + \sin^4\alpha} \\ = \dfrac{(1 - \cos^2\alpha)^2}{(1 - \sin^2\alpha)^2} \\ = \left ( \dfrac{\sin^2\alpha}{\cos^2\alpha} \right )^2 \\ = (\tan^2\alpha)^2 \\ = \tan^4\alpha = VP $