lean_workbook_plus_18380

Open

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

the maximum value of $a\sin(x) + b\cos(x)$ is $1$ when $a^2 + b^2 = 1$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_18380 (a b : ℝ) (x : ℝ) (h : a^2 + b^2 = 1) :
  a * Real.sin x + b * Real.cos x ≤ 1   :=  by sorry

Source