Although I don’t remember talking to anyone about this recently, I do know that there is a very divided opinion about whether you use “Yours sincerely” or “Yours truly” in an official letter of complaint. Some say that the latter is better, but I fail to see why the former shouldn’t work, especially because it means the same.
But before that, let’s take a look at the etymology of the word “Sincere”. A lot earlier in time, sculptors concealed imperfections in their work by pouring hot wax into the cracks of the stone. This was then covered by fine stone dust. So if you bought a sculpture that didn’t have any imperfections that needed this little covering up, you would be buying a sculpture “without wax” or sine cera, literally. It would be a sincere piece of work then. And when you sign a letter “Yours sincerely”, you tell the intended reader that what you have written is “without wax” and that your words are true.
I prefer this version more to the other etymological claim that says that the word “Sincere” is derived from the word Sinceras in Latin, literally meaning “clean/pure/of one growth”. This of course can mean that what you have written is clean, and not muddled with exaggeration or falsity, but I think the previous version works better, don’t you agree?
So then, the next time you are signing a letter, go ahead and use “Yours sincerely”. It is not different from “Yours truly” and you are not flouting any linguistic rule by using it.