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Lean-Workbook Plus 59884: Trigonometric identity

Proved
WorkbookRestored.plus_59884

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

lean-workbookrestored-importssource-checked

For every real xx, sin⁡6x+cos⁡6x−1=−3sin⁡2xcos⁡2x\sin^6x+\cos^6x-1=-3\sin^2x\cos^2x.

Source: Lean-Workbook row lean_workbook_plus_59884 (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_59884 : ∀ x : ℝ, sin x ^ 6 + cos x ^ 6 - 1 = -3 * sin x ^ 2 * cos x ^ 2   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_59884; immutable original Prove2Me node eca840f7-f064-4d6d-a934-9cf461fcf7f9

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