Đáp án:
y=-cos2x
Giải thích các bước giải:
\(\begin{array}{l}
d)y = \dfrac{{{{\left( {{{\sin }^2}x} \right)}^3} + {{\left( {{{\cos }^2}x} \right)}^3} - {{\sin }^2}x.{{\cos }^2}x}}{{{{\sin }^2}x - {{\cos }^2}x}}\\
= \dfrac{{\left( {{{\sin }^2}x + {{\cos }^2}x} \right)\left( {{{\sin }^4}x - {{\sin }^2}x{{\cos }^2}x + {{\cos }^4}x} \right) - {{\sin }^2}x.{{\cos }^2}x}}{{{{\sin }^2}x - {{\cos }^2}x}}\\
= \dfrac{{{{\sin }^4}x - {{\sin }^2}x{{\cos }^2}x + {{\cos }^4}x - {{\sin }^2}x.{{\cos }^2}x}}{{{{\sin }^2}x - {{\cos }^2}x}}\\
= \dfrac{{{{\sin }^4}x - 2{{\sin }^2}x{{\cos }^2}x + {{\cos }^4}x}}{{{{\sin }^2}x - {{\cos }^2}x}}\\
= \dfrac{{{{\left( {{{\sin }^2}x - {{\cos }^2}x} \right)}^2}}}{{{{\sin }^2}x - {{\cos }^2}x}} = {\sin ^2}x - {\cos ^2}x\\
= - \left( {{{\cos }^2}x - {{\sin }^2}x} \right) = - \cos 2x
\end{array}\)
