Prove2Me

Lean-Workbook Plus 11374: Trigonometric identity

Proved
WorkbookRestored.plus_11374

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

lean-workbookrestored-importssource-checked

For every real xx, cos⁡x=1−2sin⁡2(x/2)\cos x=1-2\sin^2(x/2).

Source: Lean-Workbook row lean_workbook_plus_11374 (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_11374 : ∀ x : ℝ, Real.cos x = 1 - 2 * (Real.sin (x / 2))^2   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_11374; immutable original Prove2Me node 2781408f-6beb-46b5-bb30-9fb59020fe4b

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