Lean-Workbook Plus 78970: Trigonometric identity

Proved

WorkbookRestored.plus_78970

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

lean-workbookrestored-importssource-checked

If $y=\sin(x+\pi/4)$ , then $\sin(2x)=2y^2-1$ .

Source: Lean-Workbook row lean_workbook_plus_78970 (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_78970 (x y : ℝ) (h₁ : y = Real.sin (x + Real.pi / 4)) : Real.sin (2 * x) = 2 * y ^ 2 - 1   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_78970; immutable original Prove2Me node 915e1fc5-b9f9-4a97-b256-f4be27e3c915

View graph