Factoring a trigonometric square difference

Proved

WorkbookRestored.plus_631

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

lean-workbookrestored-importssource-checked

For real $b,A$ ,

b^2-b^2\sin A\sin A=b^2\cos^2 A.

Formalization Note This restores source entry lean_workbook_plus_631 from the Apache-2.0 Lean-Workbook dataset. The mathematical proposition is unchanged; targeted imports and namespace openings supply the constants missing from the original Prove2Me node 27852038-bde9-4b88-a511-811533f89814. This is a separate corrected node because formal statements and preambles are immutable.

Preamble

import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
import Mathlib.Tactic
open Real

Formal statement

theorem WorkbookRestored.plus_631 (b A : ℝ) : b^2 - b^2 * Real.sin A * Real.sin A = b^2 * (Real.cos A)^2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_631; original Prove2Me theorem ID 27852038-bde9-4b88-a511-811533f89814; Apache-2.0.

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