Is $cos(\sqrt{x})$ periodic ?

Is cos (Öx) periodic ?

Graph The graph seems to show that  y = cos (Öx) is not periodic.  Can we prove that?

Proof   The proof uses the “Method of contradiction”. Assume that cos (Öx) is periodic, $ T > 0 s.t. "x ³ 0,                 In particular, we choose x = 0 and x = T,                                                           Solve (1) and (2),               where m, n are integers.            In (5), the left hand side is irrational and right hand  side is rational (note : m, n Î Z) \ There is contradiction and the given function is not periodic.

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