Lean-Workbook Plus 4774: Trigonometric identity

Proved

WorkbookRestored.plus_4774

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

lean-workbookrestored-importssource-checked

For real $b,c,\alpha$ with $\alpha\ne0,\pi$ , the area-expression identity is $16(\tfrac12bc\sin\alpha)^2=4b^2c^2\sin^2\alpha$ .

Source: Lean-Workbook row lean_workbook_plus_4774 (Apache-2.0). The unchanged proposition comes from the original record; its missing mathematical imports and namespaces are restored here.

Preamble

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

Formal statement

theorem WorkbookRestored.plus_4774 : ∀ b c : ℝ, ∀ α : ℝ, (α ≠ 0 ∧ α ≠ π) → 16 * (1 / 2 * b * c * Real.sin α) ^ 2 = 4 * b ^ 2 * c ^ 2 * (Real.sin α) ^ 2   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_4774; immutable original Prove2Me node 26898daa-356f-4db4-a007-4d08442b8207

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