Calculate $${2^{n + 1}}\prod\limits_{k = 1}^n {\cos \frac{{\pi k}}{{n + 1}}} $$
It's task in theme "Eigenvectors and eigenvalues" (linear algebra book) I have no idea.
Any advice? (How to solve it with linear algebra or mathematical analysis)
Calculate $${2^{n + 1}}\prod\limits_{k = 1}^n {\cos \frac{{\pi k}}{{n + 1}}} $$
It's task in theme "Eigenvectors and eigenvalues" (linear algebra book) I have no idea.
Any advice? (How to solve it with linear algebra or mathematical analysis)