Prove2Me

Lean-Workbook Plus 32073: Trigonometric identity

Proved
WorkbookRestored.plus_32073

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

lean-workbookrestored-importssource-checked

For every real xx, cos⁡4x=18cos⁡(4x)+12cos⁡(2x)+38\cos^4x=\tfrac18\cos(4x)+\tfrac12\cos(2x)+\tfrac38.

Source: Lean-Workbook row lean_workbook_plus_32073 (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_32073 (x : ℝ) : (cos x)^4 = 1 / 8 * cos (4 * x) + 1 / 2 * cos (2 * x) + 3 / 8   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_32073; immutable original Prove2Me node 9d0e25e9-ca42-4c77-932b-e0ca781f6e82

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