Solve :$\large\frac{dy}{dx}$$=\cos (x+y)+\sin (x+y)$.[Hint :Substitute x+y=z]

Question

$\begin{array}{1 1}(A)\;\log \bigg|1-\tan \large\frac{(x+y)}{2}\bigg|=x+c \\ (B)\;\log \bigg|1+\tan \large\frac{(x+y)}{2}\bigg|=x+c \\(C)\;\log \bigg|1+\tan \large\frac{(x+y)}{2}\bigg|=\log |x+c| \\ (D)\;\log \bigg|1-\tan \large\frac{(x+y)}{2}\bigg|=\log|x+c|\end{array} $