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Lean-Workbook Plus 60365: Trigonometric identity

Proved
WorkbookRestored.plus_60365

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

lean-workbookrestored-importssource-checked

If cos⁡(3x)=−1/2\cos(3x)=-1/2, then 8cos⁡3x−6cos⁡x+1=08\cos^3x-6\cos x+1=0.

Source: Lean-Workbook row lean_workbook_plus_60365 (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_60365 (x : ℝ) (h : Real.cos (3 * x) = -1 / 2) :
  8 * (Real.cos x)^3 - 6 * Real.cos x + 1 = 0   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_60365; immutable original Prove2Me node 6b47a0ca-c8e4-40be-a93d-ca1d3ee56336

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