\(\begin{array}{l}
E = \left( {{{\sin }^2}x + {{\cos }^2}x} \right)\left( {{{\sin }^4}x + {{\cos }^4}x - {{\sin }^2}x{{\cos }^2}x} \right) + {\sin ^4}x + {\cos ^4}x + 5{\sin ^2}x.{\cos ^2}x\\
= 2\left( {{{\sin }^4}x + {{\cos }^4}x + 2{{\sin }^2}x{{\cos }^2}x} \right)\\
= 2{\left( {{{\sin }^2}x + {{\cos }^2}x} \right)^2} = 2
\end{array}\)
\(\begin{array}{l}
F = 2{\left[ {{{\left( {{{\sin }^2}x + {{\cos }^2}x} \right)}^2} - {{\sin }^2}x{{\cos }^2}x} \right]^2} - \left[ {{{\left( {{{\sin }^4}x + {{\cos }^4}x} \right)}^2} - 2{{\sin }^4}x{{\cos }^4}x} \right]\\
= 2{\left( {1 - {{\sin }^2}x{{\cos }^2}x} \right)^2} - \left[ {{{\left( {1 - 2{{\sin }^2}x{{\cos }^2}x} \right)}^2} - 2{{\sin }^4}x{{\cos }^4}x} \right]\\
= 2\left( {1 - 2{{\sin }^2}x{{\cos }^2}x + {{\sin }^4}x{{\cos }^4}x} \right) - \left( {1 - 4{{\sin }^2}x{{\cos }^2}x + 2{{\sin }^4}x{{\cos }^4}x} \right)\\
= 2 - 1 = 1
\end{array}\)
