Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
b,\\
{\sin ^6}x + {\cos ^6}x\\
= {\left( {{{\sin }^2}x + {{\cos }^2}x} \right)^3} - 3{\sin ^2}x.{\cos ^2}x.\left( {{{\sin }^2}x + {{\cos }^2}x} \right)\\
= {1^3} - 3.si{n^2}x.{\cos ^2}x.1\\
= 1 - 3si{n^2}x.{\cos ^2}x\\
= 1 - \frac{3}{4}.{\left( {2\sin x.\cos x} \right)^2}\\
= 1 - \frac{3}{4}{\sin ^2}2x\\
= 1 - \frac{3}{4}.\frac{{1 - \cos 4x}}{2}\\
= 1 - \frac{3}{8} + \frac{3}{8}\cos 4x = \frac{5}{8} + \frac{3}{8}\cos 4x
\end{array}\)
