If $\cos (x-y), \cos x, \cos (x+y)$ are three distinct numbers which are in harmonic progression and $\cos x \neq \cos y,$ then $1+\cos y=$

Question

$$\begin {array} {1 1} (1)\;\cos ^2 x & \quad (2)\;-\cos ^2 x \\ (3)\;\cos ^2x-1 & \quad (4)\;\cos ^2 x-2 \end {array}$$