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