Lean-Workbook Plus 4399: Trigonometric identity

Proved

WorkbookRestored.plus_4399

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

lean-workbookrestored-importssource-checked

prove $\cos 3a = 4\cdot \cos^{3}a - 3\cos a$

Source: Lean-Workbook row lean_workbook_plus_4399 (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_4399 (a : ℝ) : Real.cos (3 * a) = 4 * (Real.cos a)^3 - 3 * Real.cos a   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_4399; immutable original Prove2Me node 30bdaa83-4b38-4a39-8ff5-04a09723b265

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