Lean-Workbook Plus 23560: Trigonometric inequality

Proved

WorkbookRestored.plus_23560

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

lean-workbookrestored-importssource-checked

For real $a,A$ , $a^2-2a\cos A+\cos^2 A-3\sin^2 A\le0$ if and only if $(a-\cos A+\sqrt3\sin A)(a-\cos A-\sqrt3\sin A)\le0$ .

Source: Lean-Workbook row lean_workbook_plus_23560 (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_23560 (a : ℝ) (A : ℝ) : a^2 + (-2 * Real.cos A) * a + (Real.cos A)^2 - 3 * (Real.sin A)^2 ≤ 0 ↔ (a - Real.cos A + Real.sqrt 3 * Real.sin A) * (a - Real.cos A - Real.sqrt 3 * Real.sin A) ≤ 0   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_23560; immutable original Prove2Me node 796305d9-2b19-4946-9c3e-440fe5b278ad

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