Prove2Me

Completing the square in a cosine expression

Proved
WorkbookSource.problem_9771

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

4(−cos⁡2(x)+cos⁡(x)+12)=4(−(cos⁡(x)−12)2+34)4(-\cos^2(x) + \cos(x) + \dfrac{1}{2}) = 4(-(\cos(x) - \dfrac{1}{2})^2 + \dfrac{3}{4})

Source: InternLM Lean-Workbook, record lean_workbook_9771 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble
import Mathlib
open Real Nat
Formal statement
theorem WorkbookSource.problem_9771 (x : ℝ) : 4 * (-(Real.cos x) ^ 2 + Real.cos x + 1 / 2) = 4 * (-((Real.cos x) - 1 / 2) ^ 2 + 3 / 4)  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_9771; Apache-2.0

View graph