Lean-Workbook Plus 5250: Trigonometric identity

Proved

WorkbookRestored.plus_5250

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

lean-workbookrestored-importssource-checked

Demonstrate the identity: $\sin(a+x)-\sin(a-x)=2\cos(a)\sin(x)$

Source: Lean-Workbook row lean_workbook_plus_5250 (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_5250 (a x : ℝ) : Real.sin (a + x) - Real.sin (a - x) = 2 * Real.cos a * Real.sin x   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_5250; immutable original Prove2Me node a56376b9-4548-4465-9638-fd38782aeccd

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