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Lean-Workbook Plus 66230: Trigonometric identity

Proved
WorkbookRestored.plus_66230

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

lean-workbookrestored-importssource-checked

If (sin⁡x+cos⁡x)2=π2/16(\sin x+\cos x)^2=\pi^2/16, then sin⁡xcos⁡x=(π2−16)/32\sin x\cos x=(\pi^2-16)/32.

Source: Lean-Workbook row lean_workbook_plus_66230 (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_66230 (x : ℝ) (hx : (sin x + cos x)^2 = π^2 / 4^2) : sin x * cos x = (π^2 - 16) / 32   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_66230; immutable original Prove2Me node 2837c5ba-f40b-4a50-9418-6d4b57152a0b

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