Lean-Workbook Plus 2535: Trigonometric identity

Proved

WorkbookRestored.plus_2535

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

lean-workbookrestored-importssource-checked

Prove the following identity. $\cos{2x} = 2\cos^2x - 1$

Source: Lean-Workbook row lean_workbook_plus_2535 (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_2535 : ∀ x : ℝ, Real.cos (2 * x) = 2 * (Real.cos x)^2 - 1   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_2535; immutable original Prove2Me node c9dfc668-632f-4671-88d4-5b62d89f49ef

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