Prove2Me

Lean-Workbook Plus 21175: Trigonometric identity

Proved
WorkbookRestored.plus_21175

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

lean-workbookrestored-importssource-checked

Prove the trigonometric identity: sin⁡2αcos⁡2β−cos⁡2αsin⁡2β=sin⁡2α−sin⁡2β\sin^2\alpha\cos^2\beta-\cos^2\alpha\sin^2\beta = \sin^2\alpha-\sin^2\beta

Source: Lean-Workbook row lean_workbook_plus_21175 (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_21175 (α β : ℝ) : sin α ^ 2 * cos β ^ 2 - cos α ^ 2 * sin β ^ 2 = sin α ^ 2 - sin β ^ 2   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_21175; immutable original Prove2Me node 51b9904c-7617-46ee-9033-dc67e35e6a09

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