The Chebyshev polynomials of the first kind $(T_n)_{n \in \mathbb{N}}$ are defined by $T_n(\cos\theta) = \cos(n\theta)$.
Show that the sequence $(T_n)_{n \in \mathbb{N}}$ satisfies the recurrence relation
$$\forall n \in \mathbb{N}, \quad T_{n+2} = 2X T_{n+1} - T_n$$
Deduce, for every natural integer $n$, the degree and the leading coefficient of $T_n$. Find this result again with the expression from question I.A.2.