Solution
= Solution
The recurrence and the addition formula give the result by induction. It is true for $n=0,1$, and if true for $n,n-1$, then
$$
\boxed{T_{n+1}(\cos y)=2\cos y\cos(ny)-\cos((n-1)y)=\cos((n+1)y).}
$$
= Solution
The recurrence and the addition formula give the result by induction. It is true for $n=0,1$, and if true for $n,n-1$, then
$$
\boxed{T_{n+1}(\cos y)=2\cos y\cos(ny)-\cos((n-1)y)=\cos((n+1)y).}
$$