Show that the power measures the squared correlation

Question

Question - Recall the Power function:

Power(ω_k) = (_t=1ΣⁿX_tcos(2 πω_kt))² + (_t=1Σⁿ X_t sin(2πω_kt))²

Show that the power measures the squared correlation between the data X = (X_t, t = 1,..., n)' and the sinusoidal. That is, show that Power (ω_k) = Ak · ρ^{^2} (X, U_k) + Bk · ρ^{^2} (X, V_k) where U_k = (cos(2 πω_kt), t = 1, . . . , n)' and Vk = (sin(2 πω_kt) t = 1,...,n)' , and p^{^}(X, Y) is the sample correlation between the n-dim vectors X and Y. Also, what are A_k and B_k?