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Determinant with cosines

  1. Dec 13, 2004 #1
    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.
     
  2. jcsd
  3. Dec 13, 2004 #2

    NateTG

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