Learn English – The usage of ‘Yours sincerely’ and ‘Yours faithfully’

This is called "complimentary close".

As reported by Oxford Handbook of Commercial Correspondence:

• If the letter begins with Dear Sir, Dear Sirs, Dear Madam, or Dear Sir/Madam, the COMPLIMENTARY CLOSE should be "Yours faithfully".

• If the letter begins with a personal name, e.g. Dear Mr James, Dear Mrs Robinson, or Dear Ms Jasmin, it should be "Yours sincerely".

• A letter to someone you know well may close with the more informal "Best wishes".

Note that the Americans tend to close even formal letters with Yours truly or Truly yours, which is unusual in the UK in commercial correspondence.

Avoid closing old-fashioned phrases, e.g. We remain yours faithfully, Respectfully yours.

Yours sincerely is formal but still has its place, and I would have thought that one of them was a letter applying for a position (though perhaps not an email doing the same thing).

It shows that you know how to do things properly without being as old fashioned or long winded as in I have the honour, sir, to remain your most humble and obedient servant, though you might use something similar for Queen Elizabeth II

Remember the distinction between Yours sincerely and Yours faithfully