Question

[Lê Song Phương]

Đố: Cho \(\Delta ABC\), biết \(BC=a,AC=b,AB=c,\widehat{A}=\alpha,\widehat{B}=\beta,\widehat{C}=\gamma\) chứng minh:

a)\(\frac{a}{\sin\alpha}=\frac{b}{\sin\beta}=\frac{c}{\sin\gamma}\)          b) \(a^2=b^2+c^2-2bc\cos\alpha\)

c) \(\frac{a-b}{a+b}=\frac{\tan\left[\frac{1}{2}\left(\alpha-\beta\right)\right]}{\tan\left[\frac{1}{2}\left(\alpha+\beta\right)\right]}\)         

d) Biết \(s=\frac{a+b+c}{2}\). Chứng minh \(\frac{\cot\frac{\alpha}{2}}{s-a}=\frac{\cot\frac{\beta}{2}}{s-b}=\frac{\cot\frac{\gamma}{2}}{s-c}\)