Prove2Me

Lean-Workbook Plus 33814: Trigonometric identity

Proved
WorkbookRestored.plus_33814

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

lean-workbookrestored-importssource-checked

For real A,BA,B, cos⁡(A−B)=cos⁡Acos⁡B+sin⁡Asin⁡B\cos(A-B)=\cos A\cos B+\sin A\sin B.

Source: Lean-Workbook row lean_workbook_plus_33814 (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_33814 (A B : ℝ) : Real.cos (A - B) = Real.cos A * Real.cos B + Real.sin A * Real.sin B   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_33814; immutable original Prove2Me node 7faa8836-5fde-49b5-94f6-ff8c3bedb9e9

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