How to Solve cos(x+y)dy=dx Using Trigonometric Identities?

[abrowaqas]

cos(x+y)dy=dx

I have tried to solve it by
Letting
t = x+y

But it's not going to be separated.. Some one please help..

 

[Eynstone]

Consider dx/dy. The equation becomes (1 +cost)=dt/dy.

 

[HallsofIvy]

I don't see why you would say it does not become separable. If t= x+ y then dt= dx+ dy so dy= dt- dx. cos(x+y)dy= dx becomes cos(t)(dt- dx)= cos(t)dt- cos(t)dx= dx or cos(t)dt= (1+ cos(t))dx.
dx= \frac{cos(t)}{1+ cos(t)}dt.

 

[abrowaqas]

I got the answer ..
Let u=x+y
du/dx=1+dy/dx
dy/dx=du/dx-1
Applying this:
cos(x+y)dy=dx
cos(x+y)dy/dx=1
cosu(du/dx-1)=1
du/dx-1=sec u
du/dx=1+sec u
dx/du=1/(1+sec u)
x=integral of 1/(1+sec u) du