Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
\dfrac{{{{\sin }^2}x - {{\cos }^2}x + {{\cos }^4}x}}{{{{\cos }^2}x - {{\sin }^2}x + {{\sin }^4}x}}\\
= \dfrac{{{{\sin }^2}x - \left( {1 - {{\sin }^2}x} \right) + {{\left( {1 - {{\sin }^2}x} \right)}^2}}}{{{{\cos }^2}x - \left( {1 - {{\cos }^2}x} \right) + {{\left( {1 - {{\cos }^2}x} \right)}^2}}}\\
= \dfrac{{{{\sin }^2}x - 1 + {{\sin }^2}x + \left( {1 - 2{{\sin }^2}x + {{\sin }^4}x} \right)}}{{{{\cos }^2}x - 1 + {{\cos }^2}x + \left( {1 - 2{{\cos }^2}x + {{\cos }^4}x} \right)}}\\
= \dfrac{{{{\sin }^4}x}}{{{{\cos }^4}x}} = {\tan ^4}x
\end{array}\)
