Prove2Me

lean_workbook_plus_11374

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

Prove the identity: cos⁡x=1−2sin⁡2x2\cos{x}=1-2\sin^{2}{\frac{x}{2}}.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_11374 : ∀ x : ℝ, Real.cos x = 1 - 2 * (Real.sin (x / 2))^2   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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