Prove2Me

Lean-Workbook Plus 78674: Trigonometric identity

Proved
WorkbookRestored.plus_78674

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

sin⁡x−sin⁡y=2cos⁡x+y2sin⁡x−y2\sin{x}-\sin{y}=2\cos{\frac{x+y}{2}}\sin{\frac{x-y}{2}}

Source: Lean-Workbook row lean_workbook_plus_78674 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
open Real
Formal statement
theorem WorkbookRestored.plus_78674 (x y : ℝ) : sin x - sin y = 2 * cos ((x + y) / 2) * sin ((x - y) / 2)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_78674; immutable original Prove2Me node f69493b0-c76c-4358-baca-b7ca2ee37df3

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