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Yours sincerely is used when the recipient is addressed by name and is known to you to some degree, and Yours faithfully is used when the recipient is not known by name (i.e. the recipient is addressed by a phrase such as "Dear Sir/Madam").
When the recipient's name is known, but not previously met or spoken with, some people prefer the use of the more distant Yours faithfully, but most prefer to use Yours sincerely.
In the US, "Yours sincerely" is properly used in social correspondence. "Yours faithfully" is properly used in business correspondence with someone whose name is unknown to the writer (i.e., in a letter addressed "Dear Sir or Madam" or "To Whom It May Concern").
In the US, the inverted "Sincerely yours" and the simplified "Sincerely" are also common.