$\begin{align*}A + B \cos 2 \theta = A + 2B \cos^2 \theta - B = A - B + 2 B \cos^2 \theta\end{align*}$
This is the intensity one would get if the incident light consisted of 1) light with intensity $2 B$ polarized along $\theta = 0$ and 2) unpolarized light with intensity $2(A-B)$ . In order to be able to add the intensities as we have done, we need to assume that parts 1) and 2) are incoherent. %(see Giancoli page 873-874 and 877).
Assuming this, then answer (C) is correct.

Solution to 1992 Problem 67