Lean-Workbook Plus 54215: Trigonometric identity

Proved

WorkbookRestored.plus_54215

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

lean-workbookrestored-importssource-checked

$\sin 4a = 4 \sin a \cos^{3} a - 4 \cos a \sin^{3} a$ .

Source: Lean-Workbook row lean_workbook_plus_54215 (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_54215 (a : ℝ) : Real.sin (4 * a) = 4 * Real.sin a * (Real.cos a)^3 - 4 * Real.cos a * (Real.sin a)^3   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_54215; immutable original Prove2Me node c5c3b7c7-e0bd-4517-8a77-1816f4b3750f

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