linear algebra with diagonalizable.

["mina_world"]

Hello sir~

Matrix A =

|cos@  -sin@|
|sin@   cos@ |

Show that A is diagonalizable.
Find P such that P^-1.A.P = D

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I think....
|xA - I| = x^2 - 2xcos@ + 1 = 0.

so, x = cos@ +-sqrt[(cos@)^2 - 1]

Hm...I have a trouble.
How do you solve this?