lean_workbook_plus_39832

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

Using $\sin^2 x \cos^2 x = \frac{\sin^2 2x}{4}$ and $\sin^2 x = \frac{1- \cos 2x}{2}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_39832 : ∀ x : ℝ, ((sin x)^2 * (cos x)^2) = (sin (2 * x))^2 / 4 ∧ (sin x)^2 = (1 - cos (2 * x)) / 2   :=  by sorry

Source