Lean-Workbook Plus 51560: Trigonometric identity

Proved

WorkbookRestored.plus_51560

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

lean-workbookrestored-importssource-checked

$1 - sin^{3}\theta = (1 - sin\theta)(sin^{2}\theta + sin\theta + 1)$ .

Source: Lean-Workbook row lean_workbook_plus_51560 (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_51560 (θ : ℝ) : (1 - sin θ) * (sin θ ^ 2 + sin θ + 1) = 1 - sin θ ^ 3   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_51560; immutable original Prove2Me node 411d09d1-1079-4f65-96e2-45abced7e728

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