Prove2Me

Lean-Workbook Plus 32216: Trigonometric identity

Proved
WorkbookRestored.plus_32216

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

lean-workbookrestored-importssource-checked

For real a,b,ca,b,c, cos⁡(a+b+c)+cos⁡(a+b−c)+cos⁡(a+c−b)+cos⁡(b+c−a)=4cos⁡acos⁡bcos⁡c\cos(a+b+c)+\cos(a+b-c)+\cos(a+c-b)+\cos(b+c-a)=4\cos a\cos b\cos c.

Source: Lean-Workbook row lean_workbook_plus_32216 (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_32216 {a b c : ℝ} : (Real.cos (a + b + c) + Real.cos (a + b - c) + Real.cos (a + c - b) + Real.cos (b + c - a)) = 4 * Real.cos a * Real.cos b * Real.cos c   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_32216; immutable original Prove2Me node 07bc0f71-f2ec-4ba2-8e89-cb6bcac9ba77

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