\[\begin{array}{l}
\dfrac{{{{\sin }^2}\alpha - {{\cos }^2}\alpha + {{\cos }^4}\alpha }}{{{{\cos }^2}\alpha - {{\sin }^2}\alpha + {{\sin }^4}\alpha }} = {\tan ^4}\alpha \\
VT = \dfrac{{{{\sin }^2}\alpha - {{\cos }^2}\alpha (1 - {{\cos }^2}\alpha )}}{{{{\cos }^2}\alpha - {{\sin }^2}\alpha (1 - {{\sin }^2}\alpha )}}\\
= \dfrac{{{{\sin }^2}\alpha - {{\cos }^2}\alpha {{\sin }^2}\alpha }}{{{{\cos }^2}\alpha - {{\cos }^2}\alpha {{\sin }^2}\alpha }}\\
= \dfrac{{{{\sin }^2}\alpha (1 - {{\cos }^2}\alpha )}}{{{{\cos }^2}\alpha (1 - {{\sin }^2}\alpha )}}\\
= \dfrac{{{{\sin }^4}\alpha }}{{{{\cos }^4}\alpha }} = {\tan ^4}\alpha = VP
\end{array}\]
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