Giá trị của \(T = {\cos ^4}x\;(2{\cos ^2}x - 3) + {\sin ^4}x\;(2{\sin ^2}x - 3)\) là:
A.\(1\).
B. \(0\).
C. \( - 1\).
D. \( - 2\).
Ta có: \(M \cap N = \left\{ {x|x \in M,x \in N} \right\}\).
\(\begin{array}{l}T = {\cos ^4}x\;(2{\cos ^2}x - 3) + {\sin ^4}x\;(2{\sin ^2}x - 3)\\ = 2\left( {{{\cos }^6}x + {{\sin }^6}x} \right) - 3\left( {{{\cos }^4}x + {{\sin }^4}x} \right)\\ = 2\left( {{{\cos }^2}x + {{\sin }^2}x} \right)\left( {{{\cos }^4}x - {{\cos }^2}x.{{\sin }^2}x + {{\sin }^4}x} \right) - 3\left( {{{\cos }^4}x + {{\sin }^4}x} \right)\\ = 2\left( {{{\cos }^4}x - {{\cos }^2}x.{{\sin }^2}x + {{\sin }^4}x} \right) - 3\left( {{{\cos }^4}x + {{\sin }^4}x} \right)\\ = - 2{\cos ^2}x.{\sin ^2}x - \left( {{{\cos }^4}x + {{\sin }^4}x} \right)\\ = - {\left( {{{\cos }^2}x + {{\sin }^2}x} \right)^2}\\ = - 1\end{array}\)
Chọn C
