First recorded in the Edo period. The kanji used are examples of ateji.
According to one theory, formed from 護摩 (goma) (“a holy fire in esoteric Buddhism”) + verbalizing suffix かす (kasu), from a common fraud perpetrated in the Edo period of dressing as a monk and selling regular ash purported to be ash from such holy fires.
Alternately, from 胡麻菓子 (goma kashi), from a sesame (胡麻 (goma)) candy (菓子 (kashi)) in the Edo period called 胡麻胴乱 (goma dōran) and notable for being a mostly empty shell.
Alternative forms 
誤魔化す (godan conjugation, hiragana ごまかす, romaji gomakasu)
- to cheat or deceive
- to lie
- to evade a question or deflect attention; to gloss over a mistake; to fudge; to bullshit
- to embezzle
- to defraud or swindle
- (to deceive): 欺く (あざむく, azamuku), 騙す (だます, damasu)
- (to lie): うそをつく (uso o tsuku), うそを言う (うそをいう, uso o iu): see 嘘 (uso) (“a lie”)
- (to gloss over): 取り繕う (とりつくろう, toritsukurou)
- (to embezzle): 横領する (おうりょうする, ōryō suru)
- (to defraud): 詐取する (さしゅする, sashu suru), 騙し取る (だましとる, damashitoru)