Prove2Me

Lean-Workbook Plus 49730: Trigonometric identity

Proved
WorkbookRestored.plus_49730

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

lean-workbookrestored-importssource-checked

For real x,y,zx,y,z, sin⁡(x−y)sin⁡(z−x)=12(cos⁡(2x−y−z)−cos⁡(z−y))\sin(x-y)\sin(z-x)=\tfrac12(\cos(2x-y-z)-\cos(z-y)).

Source: Lean-Workbook row lean_workbook_plus_49730 (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_49730 (x y z : ℝ) : Real.sin (x - y) * Real.sin (z - x) = 1/2 * (Real.cos (2 * x - y - z) - Real.cos (z - y))   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_49730; immutable original Prove2Me node ad9a8cee-97b6-446c-bf20-982843666933

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