Sentence-ending expression seeking agreement or confirmation, similar to a tag question. Often used when the speaker expects the listener to agree.
This is delicious, isn't it?
let's ...; why don't we ...; shouldn't we ...
Follows the volitional form of a verb to make a suggestion or invitation. Softer than a direct command.
Why don't we get going?
He already went home, didn't he?
一緒に食べようではないか。
Let's eat together, shall we?
じゃないか is the casual, contracted form used in informal speech, while ではないか is the fuller, slightly more formal or literary form of the same tag-question/suggestion expression.
だろう expresses plain conjecture or seeks simple agreement, whereas ではないか carries an extra nuance of mild surprise, discovery, or emphasis when confirming something.
ではないか is a more formal or written-sounding version of the same confirmation pattern, whereas ちゃうか is casual Kansai dialect speech.
ではないか is the formal or written counterpart of じゃないか, used in polite speech or formal writing where じゃないか would be too casual.
From the negative form of the copula だ (では) + ない + question particle か. The kanji spelling では無いか is a literal representation but rarely used.