[Cẩm Lynh]

Cho tam giác $ABC$. Chứng minh rằng

1. $
   \dfrac{1}{\sin A}+\dfrac{1}{\sin B}+ \dfrac{1}{\sin C} \geq \dfrac{1}{\cos \frac{A}{2}}+\dfrac{1}{\cos \frac{B}{2}}+\dfrac{1}{\cos \frac{C}{2}}
   $.
2. $\dfrac{1}{\sin^nA}+\dfrac{1}{\sin^nB}+\dfrac{1}{ \sin^n C} \geq \dfrac{1}{\cos^n \frac{A}{2}}+\dfrac{1}{\cos^n \frac{B}{2}}+\dfrac{1}{\cos^n \frac{C}{2}}, \ n \in \mathbb{N}^*$.

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[RIGHT][I][B]Nguồn: MathScope.ORG[/B][/I][/RIGHT]