Rút gọn các biểu thức a) E = (1 − sin^2 α cos^2 α)/ cos^2 α − cos^2 α .

a) \(E = \frac{{1 - {{\sin }^2}\alpha {{\cos }^2}\alpha }}{{{{\cos }^2}\alpha }} - {\cos ^2}\alpha \)\( = \frac{1}{{{{\cos }^2}\alpha }} - {\sin ^2}\alpha - {\cos ^2}\alpha \)\( = \frac{1}{{{{\cos }^2}\alpha }} - 1\)\( = \frac{{1 - {{\cos }^2}\alpha }}{{{{\cos }^2}\alpha }} = {\tan ^2}\alpha \).

b) \(F = 2\left( {{{\sin }^4}x + {{\cos }^4}x} \right) + 4{\sin ^2}x{\cos ^2}x\)\( = 2\left( {{{\sin }^4}x + {{\cos }^4}x + 2{{\sin }^2}x{{\cos }^2}x} \right)\)

\( = 2{\left( {{{\sin }^2}x + {{\cos }^2}x} \right)^2} = 2\).