Integrate : $\int \large\frac{\cos 2x - \cos 2 \alpha}{\cos x - \cos \alpha}$$ dx $

Question

\[\begin {array} {1 1} (a)\;2 (\sin x + x \sin \alpha)+c \\ (b)\; 2 ( \sin \alpha + x \cos \alpha)+c \\ (c)\;2 ( \sin x + x \cos \alpha)+c \\ (d)\;2 (\sin x + \sin \alpha )+c \end {array}\]