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

Question

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