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Lean-Workbook Plus 17252: Trigonometric identity

Proved
WorkbookRestored.plus_17252

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

lean-workbookrestored-importssource-checked

Prove that sin⁡2α−sin⁡2β=sin⁡(α+β)⋅sin⁡(α−β)\sin^2\alpha-\sin^2\beta=\sin(\alpha+\beta)\cdot \sin(\alpha-\beta)

Source: Lean-Workbook row lean_workbook_plus_17252 (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_17252 (α β : ℝ) : (sin α) ^ 2 - (sin β) ^ 2 = sin (α + β) * sin (α - β)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_17252; immutable original Prove2Me node 9ae715b4-942d-434c-8fe4-2ef998b3a040

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