The solution of the differential equation $\large\frac{dy}{dx}$$=\sin (x+y) \tan (x+y)-1$ is :

Question

$$\begin {array} {1 1} (1)\;cosec (x+y)+ \tan (x+y)=x+c & \quad (2)\;x+cosec (x+y)=c \\ (3)\;x+\tan (x+y)=c & \quad (4)\;x+\sec(x+y)=c \end {array}$$