Prove2Me

Lean-Workbook Plus 77082: Trigonometric identity

Proved
WorkbookRestored.plus_77082

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

lean-workbookrestored-importssource-checked

For real xx with cos⁡x≠0\cos x\ne0, sin⁡(2x)/cos⁡x=2sin⁡x\sin(2x)/\cos x=2\sin x.

Source: Lean-Workbook row lean_workbook_plus_77082 (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_77082  (x : ℝ)
  (h₀ : cos x ≠ 0) :
  sin (2 * x) / cos x = 2 * sin x   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_77082; immutable original Prove2Me node e4761a13-d769-4158-bbff-bb3af5a32a4e

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