lean_workbook_plus_41954

Open

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

证明： $\frac{\cos A\cos B}{ab} + \frac{\cos B\cos C}{bc} + \frac{\cos A\cos C}{ac} = \frac{(\sin A)^2}{a^2}$ ，其中 $A+B+C=180^{\circ}$ 。

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_41954 (A B C a b c : ℝ) (ha : a > 0) (hb : b > 0) (hc : c > 0) (hab : a + b > c) (hbc : b + c > a) (hca : a + c > b) (hA: 0 < A ∧ A <= π ∧ cos A = (b^2 + c^2 - a^2)/(2*b*c))  (hB: 0 < B ∧ B <= π ∧ cos B = (a^2 + c^2 - b^2)/(2*a*c)) (hC: 0 < C ∧ C <= π ∧ cos C = (a^2 + b^2 - c^2)/(2*a*b)) : (cos A * cos B)/(a * b) + (cos B * cos C)/(b * c) + (cos A * cos C)/(a * c) = (sin A)^2/(a^2)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph