aoshima

I tried the recursion, but I have no idea to connect it to the cosine .

Given a matrix in the following form [math] H \begin{bmatrix} 0&1 & \\ 1&0& 1 \\ &1 &0 & 1 \\ &&\ddots &0& \ddots\\ &&&1&0 & 1 \\ &&&&1&0 \\ \end{bmatrix}_N [/math] ,how to prove that the eigen value of the matrix H are ? [math] E=2\cos\left( \frac{n\pi}{N+1} \right); \quad n = 1, 2, \dots , N [/math] Help:confused::confused: