Soothe
Old English sōthian ‘verify, show to be true’, from sōth ‘true’ (see sooth). In the 16th century the verb passed through the senses ‘corroborate (a statement’), ‘humour (a person) by expressing assent’ and ‘flatter by one's assent’, whence ‘mollify, appease’ (late 17th century).
wiktionary
From Middle English sothen(“to verify, prove the validity of”), from Old English sōþian(“to verify, prove, confirm, bear witness to”), from Proto-Germanic *sanþōną(“to prove, certify, acknowledge, testify”), from Proto-Indo-European *h₁es-(“to be”). Cognate with Danish sande(“to verify”), Swedish sanna(“to verify”), Icelandic sanna(“to verify”), Gothic 𐍃𐌿𐌸𐌾𐌰𐌽( suþjan), 𐍃𐌿𐌸𐌾𐍉𐌽( suþjōn, “to soothe”). See also: sooth.
etymonline
soothe (v.)
Old English soðian "show to be true," from soð "true" (see sooth). Sense of "quiet, comfort, mollify" is first recorded 1690s, via notion of "to assuage one by asserting that what he says is true" (i.e. to be a yes-man), a sense attested from 1560s (and compare Old English gesoð "a parasite, flatterer"). Meaning "reduce the intensity" (of a pain, etc.) is from 1711. Related: Soothed; soothing.