grandes-ecoles 2010 QI.A.2

grandes-ecoles · France · centrale-maths1__pc Addition & Double Angle Formulae Trigonometric Identity Proof or Derivation
For every integer $n \in \mathbb{N}$, we set $F_n(x) = \cos(n \arccos x)$.
Calculate $F_{n+1}(x) + F_{n-1}(x)$ for all $n \in \mathbb{N}^*$ and all $x \in D$.
For every integer $n \in \mathbb{N}$, we set $F_n(x) = \cos(n \arccos x)$.

Calculate $F_{n+1}(x) + F_{n-1}(x)$ for all $n \in \mathbb{N}^*$ and all $x \in D$.