From 《诗经·卫风·氓》: 言笑晏晏，信誓旦旦 — a betrayed woman remembers her ex-lover's warm smiles and solemn vows. The idiom already carried a tinge of irony in its source text: the vows were sincere and still got broken.
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Often faintly ironic in modern use — when you say someone 信誓旦旦ed, there's a good chance you're about to point out they didn't follow through. Use carefully when the commitment was actually kept.
