Prove2Me

Lean-Workbook Plus 25895: Trigonometric identity

Proved
WorkbookRestored.plus_25895

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

lean-workbookrestored-importssource-checked

If cos⁡x−cos⁡y=1/5\cos x-\cos y=1/5, then −2sin⁡((x+y)/2)sin⁡((x−y)/2)=1/5-2\sin((x+y)/2)\sin((x-y)/2)=1/5.

Source: Lean-Workbook row lean_workbook_plus_25895 (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_25895 (x y : ℝ) (h : cos x - cos y = 1 / 5) :
  -2 * sin ((x + y) / 2) * sin ((x - y) / 2) = 1 / 5   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_25895; immutable original Prove2Me node bdae1187-3ea3-4b55-809e-83be3c57be82

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