Sincere
mid 16th century (also in the sense ‘not falsified, unadulterated’): from Latin sincerus ‘clean, pure’.
wiktionary
From Middle French sincere, from Latin sincerus(“genuine”), from Proto-Indo-European *sin- + *ḱer-(“grow”), from which also Ceres(“goddess of harvest”) from which English cereal.
Unrelated to sine(“without”) cera(“wax”) (folk etymology); see Wikipedia discussion.
etymonline
sincere (adj.)
1530s, "pure, unmixed," from French sincere (16c.), from Latin sincerus, of things, "whole, clean, pure, uninjured, unmixed," figuratively "sound, genuine, pure, true, candid, truthful," of uncertain origin. The 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" (from PIE root *ker- (2) "to grow"). De Vaan finds plausible a source in a lost adjective *caerus "whole, intact," from a PIE root meaning "whole."
