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Lean-Workbook Plus 32385: Trigonometric identity

Proved
WorkbookRestored.plus_32385

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

lean-workbookrestored-importssource-checked

For every real xx, sin⁡4x−cos⁡4x=−cos⁡(2x)\sin^4x-\cos^4x=-\cos(2x).

Source: Lean-Workbook row lean_workbook_plus_32385 (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_32385 : ∀ x : ℝ, sin x ^ 4 - cos x ^ 4 = -cos (2 * x)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_32385; immutable original Prove2Me node 09c3ddc1-4351-4b14-8caa-3a71416e8195

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