Chứng minh với mọi tam giác $ABC$ thì ta luôn có:$\frac{\cos (\frac{B}{2}-\frac{C}{2})}{\sin \frac{A}{2}}+\frac{\cos (\frac{C}{2}-\frac{A}{2})}{\sin \frac{B}{2}}+\frac{\cos (\frac{A}{2}-\frac{B}{2})}{\sin \frac{C}{2}}$$\leq 2(\frac{\tan \frac{A}{2}}{\tan \frac{B}{2}}+\frac{\tan \frac{B}{2}}{\tan\frac{C}{2}}+\frac{\tan \frac{C}{2}}{\tan \frac{A}{2}})$