lean_workbook_plus_56140

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by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that:\n\n $(1+\cos\theta)(1+\cos\alpha) = 4\cos^{2}\frac{\theta}{2}\cos^{2}\frac{\alpha}{2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_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