A quadratic bound for cosine

Proved

WorkbookSource.problem_19231

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Now, $\cos A(1 - \cos A)\le \frac 14\ \Longleftrightarrow\ \cos A - \cos^2 A - \frac 14\le 0$

Source: InternLM Lean-Workbook, record lean_workbook_19231 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_19231 : ∀ A : ℝ, Real.cos A * (1 - Real.cos A) ≤ 1 / 4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_19231; Apache-2.0

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