Question

We use 'Yours sincerely' or 'Sincerely urs.' at the end of a letter. Then what is the full form of 'Yours sincerely'?

1. I am your sincerely friend.
2. I am your sincerely servant.
3. I am your sincerely friend/servant.
4. I am your friend/servant sincerely.

Answer 1

Probably the last one is the closest. I've always taken that to mean "I am sincerely at your service." Sounds a bit weird, but then idioms usually are!

Answer 2

I don't think any of them is the full form.

Since "Sincerely yours" is used at the end of different kinds of letters, we don't assume that we mean either "friend" or "servant."

This site has a brief discussion of this term.

http://www.dailywritingtips.com/yours-faithfully-or-yours-sincerely/