Prove2Me

Lean-Workbook Plus 11950: Trigonometric identity

Proved
WorkbookRestored.plus_11950

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

lean-workbookrestored-importssource-checked

For every real xx, cos⁡(3x)=cos⁡x (1−4sin⁡2x)\cos(3x)=\cos x\,(1-4\sin^2 x).

Source: Lean-Workbook row lean_workbook_plus_11950 (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_11950 x : Real.cos (3 * x) = Real.cos x * (1 - 4 * (Real.sin x)^2)   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_11950; immutable original Prove2Me node f5d86adc-75b9-4f41-9498-9bcfb0e60a62

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