Trying to find the general solution to this homogeneous difference equation:
$y_k - 2\cos\theta y_{k-1} + y_{k-2} = 0.$
The characteristic equation is
$\lambda^2 - 2\cos\theta \lambda + 1 = 0.$
Not sure how to factor this, but tried
$(\lambda - \cos\theta)(\lambda - \cos\theta) = 0$
but I am stuck as to how to get $\cos^2\theta = 1$ using trigonometric identities.
By using the quadratic formula I get a discriminant of
$4(\cos^2\theta - 1)$
and I am stuck on how to simplify this to get the general solution.
Any help is appreciated. This is not for homework, but self study.