Let $a > 0$, $I = [-a, a]$. For all $n \in \mathbb { N } ^ { * }$, the Chebyshev points of order $n$ in $I$ are
$$a _ { k , n } ^ { * } = a \cos \left( \frac { ( 2 k - 1 ) \pi } { 2 n } \right) , \quad \text { for } k \in \llbracket 1 , n \rrbracket ,$$
and $W _ { n } ^ { * } ( X ) = \prod _ { k = 1 } ^ { n } \left( X - a _ { k , n } ^ { * } \right)$. For all $x \in [ - a , a ]$, show that $\left| W _ { n } ^ { * } ( x ) \right| \leqslant 2 \left( \frac { a } { 2 } \right) ^ { n }$.