Determinant with cosines

[Nobody1111]

Proof, that determinant (with n rows and columns)

| cosx 1 0 0 ... 0 0 |
| 1 2cosx 1 0 ... 0 0 |
| 0 1 2cosx 1 ... 0 0 |
| 0 0 1 2cosx ... 0 0 | = cos nx
|.......................... |
| 0 0 0 0 ... 2cosx 1 |
| 0 0 0 0 ... 1 2cosx |

The main proble for me is to evaluate this determinant.

Do you have any ideas?

Thanks for help.

[NateTG]

It looks a lot like you want to use induction on the number of rows&columns.