Lean-Workbook Plus 4637: Trigonometric identity

Proved

WorkbookRestored.plus_4637

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

lean-workbookrestored-importssource-checked

The expression $-\tfrac12(\cos 1-\cos 0)$ equals $(1-\cos 1)/2$ .

Source: Lean-Workbook row lean_workbook_plus_4637 (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_4637 :
  -(1 / 2) * (Real.cos 1 - Real.cos 0) = (1 - Real.cos 1) / 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_4637; immutable original Prove2Me node 2f6b15f4-7075-42d4-a752-a73db775e2c3

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