That is a great question! Some background info:
- the Accounts & Sync sections stores login credentials for apps. They can be reused by other apps, e.g. Google Plus asks for pemission to access your gmail credentials.
- no browser I know of currently integrates with these account credentials. Even if they did, they would have to somehow link the site with the correct account (or ask the user to do this)
- browsers can however store cookies (hence not needing you to login each time), so if you tick the 'remember me' on login on most sites, that will do the trick
- browsers can also save your username and password into its own store. It will normally ask you when you login if you want it to store the credentials. I sometimes allow this for convenience.
So in short, browsers won't use the apps login credentials (although it would be awesome if they did for popular apps like twitter, facebook, linkedin, etc). There is no technical limitation there. You can however use browser cookies or password storage, or look into password mangers like LastPass (search market for password manager). I am actually gonna try a few now to see if they are any good.
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