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Lean-Workbook Plus 79998: Trigonometric identity

Proved
WorkbookRestored.plus_79998

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

lean-workbookrestored-importssource-checked

For every real xx, sin⁡4x=3/8−(4/8)cos⁡(2x)+(1/8)cos⁡(4x)\sin^4x=3/8-(4/8)\cos(2x)+(1/8)\cos(4x).

Source: Lean-Workbook row lean_workbook_plus_79998 (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_79998 (x : ℝ) : (sin x)^4 = 3/8 - 4/8 * cos (2 * x) + 1/8 * cos (4 * x)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_79998; immutable original Prove2Me node 5924b96e-1f1f-4497-8d22-716390563b31

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