Q:

Determine if the given differential equation is separable

I tried to solve this equation $dy/dx-\sin(x+y)=0$ but I don't know if is separable or not. 
I did alternate form $dy/dx = (\sin x\cos y)+(\cos x\sin y)$.
Then i used trigonometry identities and algebra to simplify the equation. 
$$(1/\sin x)dy/dx=\cos y+((\cos x\sin y)/\sin x)$$
$$(1/\sin y)(dy/\sin xdx)=\cos y+\cot x$$
$$dy/\sin x\sin ydx=(\cos y/\sin y)+\cot x$$
$$dy/\sin x\sin ydx=\cot y+\cot x$$
$$dy/dx=(\cot y+\cot x)(\sin x\sin y)$$
$$dy/dx=\cos y\sin x+\cos x\sin y$$
Then i suppose the "solution" should be integral of
$dy/(\cos y\sin y)=(\sin x+\cos x)dx$ ?? 
Please help me.  

A:

$$
\frac{dy}{dx} = \sin(x+y)
$$
let $v = y+x$ we find
$$
v' - 1 = \sin v
$$
thus we know that it is separable, and approachable by using $\tan$ substitution. 