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Lean-Workbook Plus 40973: Trigonometric identity

Proved
WorkbookRestored.plus_40973

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

lean-workbookrestored-importssource-checked

For every real xx, x2−x(sin⁡x+cos⁡x)+sin⁡xcos⁡x=(x−sin⁡x)(x−cos⁡x)x^2-x(\sin x+\cos x)+\sin x\cos x=(x-\sin x)(x-\cos x).

Source: Lean-Workbook row lean_workbook_plus_40973 (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_40973 (x : ℝ) : x^2 - x * (sin x + cos x) + sin x * cos x = (x - sin x) * (x - cos x)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_40973; immutable original Prove2Me node 155679ae-0397-4c10-8892-e48c29f36be1

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