Solution
= Solution
The recurrence shows that $T_n$ is a <polynomial> with integer coefficients. Part (a) gives
$$
T_n(\cos(\pi/n))+1=\cos\pi+1=0.
$$
\b[Thus $\cos(\pi/n)$ is a root of a nonzero integer <polynomial> and is algebraic.]
= Solution
The recurrence shows that $T_n$ is a <polynomial> with integer coefficients. Part (a) gives
$$
T_n(\cos(\pi/n))+1=\cos\pi+1=0.
$$
\b[Thus $\cos(\pi/n)$ is a root of a nonzero integer <polynomial> and is algebraic.]