Prove2Me

Lean-Workbook Plus 9324: Trigonometric identity

Proved
WorkbookRestored.plus_9324

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

lean-workbookrestored-importssource-checked

If sin⁡a+cos⁡a=1/5\sin a+\cos a=1/5, then sin⁡3a+cos⁡3a=37/125\sin^3a+\cos^3a=37/125.

Source: Lean-Workbook row lean_workbook_plus_9324 (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_9324 (a : ℝ) (h : sin a + cos a = 1/5) : sin a ^ 3 + cos a ^ 3 = 37/125   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_9324; immutable original Prove2Me node 5c695bb4-8738-47af-8d80-8b805b7477fc

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