using different domain for static contents?

Question

Say my web server is named example.com

now I want to use cloudflare cdn for media.example.com .

but cloudflare requires to change example.com 's name server to cloudflare's, and I can't do that

I could instead use media.another.com instead of media.example.com . (They only point to s3 bucket)

Question is, is it fine to use example.com for web service and media.another.com for a static contents it serves?

can the host differ? (I know javascript ajax requests don't allow crossing the site, and I wonder something similar is at play here? )

Answer 1

It is not only Ook, it is recommended because this way there is no way cookies from the original domain are sent on every request (which possibly adds a LOT of size to every request).