Demonstrate that the difference equation given in (4.5.52) can be obtained by applying the trigonometric identity, where ? = (n + 1) ?₀, ? = (n ? 1) ?₀, and y(n) = cos ?₀n. Thus shown that the sinusoidal signal y (n) = A cos ?₀n can be generated from (4.5.52) by using of the initial condition y (- 1) = A cos ?₀ and y (-2) = A cos 2 ?₀.

(4.5.52) y(n) = -aiy(n - 1) - y(n - 2) cos a + cos B = 2 cos Cos 2