Cho $\begin{cases}x_{n}= \cos \alpha_{1}.\cos \alpha_{2}...\cos \alpha_{n-2}.\cos \alpha_{n-1}\\ x_{n-1}= \cos \alpha_{1}.\cos \alpha_{2}...\cos \alpha_{n-2}.\sin \alpha_{n-1} \\ x_{n-2}= \cos \alpha_{1}.\cos \alpha_{2}...\cos \alpha_{n-3}.\sin \alpha_{n-2} \\ ......................................... \\ x_{2}=\cos \alpha_{1}.\sin \alpha_{2} \\ x_{1}=\sin \alpha_{1} \left ( n \in Z,n\geq 3 \right )\end{cases} $
Chứng minh rằng:
${x_{1}}^{4}+{x_{2}}^{4}+...+{x_{n}}^{4}\geq \frac{1}{n}$
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