Lean-Workbook Plus 27520: Trigonometric identity

Proved

WorkbookRestored.plus_27520

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

lean-workbookrestored-importssource-checked

For every real $x$ , $\cos(3x)-\cos(5x)=2\sin x\sin(4x)$ .

Source: Lean-Workbook row lean_workbook_plus_27520 (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_27520 (x : ℝ) :
  Real.cos (3 * x) - Real.cos (5 * x) = 2 * Real.sin x * Real.sin (4 * x)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_27520; immutable original Prove2Me node 718537aa-1d88-48ee-95fc-2a415706697c

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