lean_workbook_plus_51013

For those who don't know derivatives, \nuse the fact that, \n $(a+b+c)^2 \geq 3(ab+bc+ca)$ \nwhich gives, \n $\left(\tan\frac{A}{2}+\tan\frac{B}{2}+\tan\frac{C}{2}\right)^2 \geq 3(\tan\frac{A}{2}\tan\frac{B}{2}+\tan\frac{B}{2}\tan\frac{C}{2}+\tan\frac{C}{2}\tan\frac{A}{2})$ \nand \nthe well known identity, \n $\tan\frac{A}{2}\tan\frac{B}{2}+\tan\frac{B}{2}\tan\frac{C}{2}+\tan\frac{C}{2}\tan\frac{A}{2}=1$