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Lean-Workbook Plus 17577: Trigonometric identity

Proved
WorkbookRestored.plus_17577

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

lean-workbookrestored-importssource-checked

For every real xx, x2+6=(xcos⁡x−3sin⁡x)(xcos⁡x−2sin⁡x)−(xsin⁡x+3cos⁡x)(−xsin⁡x−2cos⁡x)x^2+6=(x\cos x-3\sin x)(x\cos x-2\sin x)-(x\sin x+3\cos x)(-x\sin x-2\cos x).

Source: Lean-Workbook row lean_workbook_plus_17577 (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_17577 : ∀ x : ℝ, x^2 + 6 = (x * cos x - 3 * sin x) * (x * cos x - 2 * sin x) - (x * sin x + 3 * cos x) * (-x * sin x - 2 * cos x)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_17577; immutable original Prove2Me node 1554b22d-e66f-4df0-849e-87817c7f2464

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