Prove2Me

Lean-Workbook Plus 47859: Trigonometric inequality

Proved
WorkbookRestored.plus_47859

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

lean-workbookrestored-importssource-checked

For 0<θ<π/20<\theta<\pi/2, tan⁡θ(1−sin⁡θ)<2\tan\theta(1-\sin\theta)<2.

Source: Lean-Workbook row lean_workbook_plus_47859 (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_47859 (θ : ℝ) (h1 : 0 < θ) (h2 : θ < Real.pi / 2) : 2 > Real.tan θ * (1 - Real.sin θ)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_47859; immutable original Prove2Me node c1ccb860-9d4c-47e9-b36d-e72b287c5207

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