Prove2Me

Lean-Workbook Plus 19668: Trigonometric identity

Proved
WorkbookRestored.plus_19668

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

lean-workbookrestored-importssource-checked

For all real x,yx,y, cos⁡x−cos⁡y=−2sin⁡((x+y)/2)sin⁡((x−y)/2)\cos x-\cos y=-2\sin((x+y)/2)\sin((x-y)/2).

Source: Lean-Workbook row lean_workbook_plus_19668 (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_19668 : ∀ x y : ℝ, Real.cos x - Real.cos y = -2 * Real.sin ((x + y) / 2) * Real.sin ((x - y) / 2)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_19668; immutable original Prove2Me node 445b5f01-4bc3-4eae-96c4-4790a6ff0cd8

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