Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
{\sin ^6}\dfrac{x}{2} - {\cos ^6}\dfrac{x}{2}\\
= \left( {{{\sin }^2}\dfrac{x}{2} - {{\cos }^2}\dfrac{x}{2}} \right).\left( {{{\sin }^4}\dfrac{x}{2} + {{\sin }^2}\dfrac{x}{2}.{{\cos }^2}\dfrac{x}{2} + {{\cos }^4}\dfrac{x}{2}} \right)\\
= - \left( {{{\cos }^2}\dfrac{x}{2} - {{\sin }^2}\dfrac{x}{2}} \right).\left[ {{{\left( {{{\sin }^2}\dfrac{x}{2} + {{\cos }^2}\dfrac{x}{2}} \right)}^2} - {{\sin }^2}\dfrac{x}{2}.{{\cos }^2}\dfrac{x}{2}} \right]\\
= - \cos x.\left[ {{1^2} - \dfrac{1}{4}.{{\left( {2\sin \dfrac{x}{2}.\cos \dfrac{x}{2}} \right)}^2}} \right]\\
= - \cos x.\left( {1 - \dfrac{1}{4}{{\sin }^2}x} \right)\\
= \dfrac{1}{4}\cos x.\left( {{{\sin }^2}x - 4} \right)
\end{array}\)
