sincere (adj.)youdaoicibaDictYouDict[sincere 词源字典]
1530s, "pure, unmixed," from Middle French sincere (16c.), from Latin sincerus, of things, "whole, clean, pure, uninjured, unmixed," figuratively "sound, genuine, pure, true, candid, truthful," of uncertain origin. Ground sense seems to be "that which is not falsified." Meaning "free from pretense or falsehood" in English is from 1530s.

There has been a temptation to see the first element as Latin sine "without." But there is no etymological justification for the common story that the word means "without wax" (*sin cerae), which is dismissed out of hand by OED and others, and the stories invented to justify that folk etymology are even less plausible. Watkins has it as originally "of one growth" (i.e. "not hybrid, unmixed"), from PIE *sm-ke-ro-, from *sem- "one" (see same) + root of crescere "to grow" (see crescent).[sincere etymology, sincere origin, 英语词源]