lean_workbook_plus_21175

Open

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

Prove the trigonometric identity: $\sin^2\alpha\cos^2\beta-\cos^2\alpha\sin^2\beta = \sin^2\alpha-\sin^2\beta$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_21175 (α β : ℝ) : sin α ^ 2 * cos β ^ 2 - cos α ^ 2 * sin β ^ 2 = sin α ^ 2 - sin β ^ 2   :=  by sorry

Source