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Lean-Workbook Plus 5029: Trigonometric identity

Proved
WorkbookRestored.plus_5029

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

lean-workbookrestored-importssource-checked

Prove that 3sin⁡a−4sin⁡3a=sin⁡3a3 \sin a - 4 \sin^{3}a = \sin 3a.

Source: Lean-Workbook row lean_workbook_plus_5029 (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_5029 (a : ℝ) : 3 * Real.sin a - 4 * (Real.sin a)^3 = Real.sin (3 * a)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_5029; immutable original Prove2Me node 255d26ea-bcd0-4d81-bf38-e7d0d2a5042b

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