Do I capitalize "sincerely" in a correspondence signature?
You should capitalize only the first word in salutation, as in
Dear Mr. X
My dear Mr. X
and also, only the first word of closing
Sincerely
Very truly yours
The salutation and closing of a business letter are formulaic sentences, nothing more. That is, there is very little variation in salutations and closings from one business letter to another. But the rules for sentence construction, capitalization, and punctuation still apply. You will normally see the salutation and closing capitalized because they are normally the start of a new sentence.