Solution of the general equation : $\large\frac{dy}{dx}$$=\cos (x+y) - \sin (x+y)$

Question

$(a)\;\log (1- \tan (\frac{x+y}{2}))+x=c \\ (b)\;\log (1+\tan (\frac{x+y}{2}))+x=c \\ (c)\;\log (1+\tan (\frac{x+y}{2}))-x=c \\ (d)\;\log (1- \tan (\frac{x+y}{2}))-x=c$