Prove2Me

Lean-Workbook Plus 25208: Trigonometric identity

Proved
WorkbookRestored.plus_25208

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

lean-workbookrestored-importssource-checked

For every natural number nn, 2cos⁡(π/2n+1)+2=4cos⁡2(π/2n+2)2\cos(\pi/2^{n+1})+2=4\cos^2(\pi/2^{n+2}).

Source: Lean-Workbook row lean_workbook_plus_25208 (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_25208 : ∀ n : ℕ, 2 * Real.cos (π / 2 ^ (n + 1)) + 2 = 4 * (Real.cos (π / 2 ^ (n + 2))) ^ 2   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_25208; immutable original Prove2Me node 0cbc34ae-924a-40dc-b992-e930a947a072

View graph