Neka su
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
,
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
i
![c](/media/m/e/a/3/ea344283b6fa26e4a02989dd1fb52a51.png)
stranice trokuta te
![\alpha](/media/m/f/c/3/fc35d340e96ae7906bf381cae06e4d59.png)
,
![\beta](/media/m/c/e/f/cef1e3bcf491ef3475085d09fd7d291e.png)
i
![\gamma](/media/m/2/4/a/24aca7af13a8211060a900a49ef999e9.png)
njima nasuprotni kutovi, redom. Dokaži da vrijedi
%V0
Neka su $a$, $b$ i $c$ stranice trokuta te $\alpha$, $\beta$ i $\gamma$ njima nasuprotni kutovi, redom. Dokaži da vrijedi $$
(\sin \alpha + \sin \beta + \sin \gamma ) \cdot
( \ctg \alpha + \ctg \beta + \ctg \gamma)\\
=\dfrac{1}{2} (a^2+b^2+c^2) \cdot
\left(\dfrac{1}{ab}+\dfrac{1}{ac}+\dfrac{1}{bc}\right).
$$