Prove2Me

Lean-Workbook Plus 56140: Trigonometric identity

Proved
WorkbookRestored.plus_56140

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

lean-workbookrestored-importssource-checked

For real α,θ\alpha,\theta, (1+cos⁡θ)(1+cos⁡α)=4cos⁡2(θ/2)cos⁡2(α/2)(1+\cos\theta)(1+\cos\alpha)=4\cos^2(\theta/2)\cos^2(\alpha/2).

Source: Lean-Workbook row lean_workbook_plus_56140 (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_56140 (α θ : ℝ) : (1 + Real.cos θ) * (1 + Real.cos α) = 4 * (Real.cos (θ / 2))^2 * (Real.cos (α / 2))^2   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_56140; immutable original Prove2Me node 1c1d980e-94a9-4de6-a36c-d4cc5888bfea

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