In any , prove that A B + C - A 3 and the equality holds if and only if triangle is…

MATHEMATICS · Subjective · AoPS · Mathematics · More Inequalities · More Inequalities

Problem

In any

\Delta ABC

, prove that

\Sigma \frac{\sqrt{\sin A}}{\sqrt{\sin B} + \sqrt{\sin C} - \sqrt{\sin A}} \ge 3

and the equality holds if and only if triangle is equilateral.