[tex]\dfrac{\sin^4(\alpha)+\cos^4(\alpha)-1}{\sin^6(\alpha)+\cos^6(\alpha)-1} = \dfrac{\sin^4(\alpha)+\cos^4(\alpha)-(\sin^2(\alpha)+\cos^2(\alpha))}{\Big(\sin^2(\alpha)\Big)^3+\Big(\cos^2(\alpha)\Big)^3-1} = \\ \\ = \dfrac{\sin^2(\alpha) \Big(\sin^2(\alpha)-1\Big)+\cos^2(\alpha)\Big(\cos^2(\alpha)-1\Big)}{\Big(\sin^2(\alpha)+\cos^2(\alpha)\Big)\Big(\sin^4(\alpha)-\sin^2(\alpha)\cos^2(\alpha)+\cos^4(\alpha)\Big)-1} =[/tex]
[tex]\\ \\ = \dfrac{-\sin^2(\alpha)\cos^2(\alpha)-\cos^2(\alpha)\sin^2(\alpha)}{-\sin^2(\alpha)\cos^2(\alpha)-\cos^2(\alpha)\sin^2(\alpha)-\sin^2(\alpha)\cos^2(\alpha)} = \\ \\ = \dfrac{-2\Big(\sin(\alpha)\cos(\alpha)\Big)^2}{-3\Big(\sin(\alpha)\cos(\alpha)\Big)^2} = \dfrac{2}{3}[/tex]
