Dokaži da u trokutu
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
s duljinama stranica
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
,
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
,
![c](/media/m/e/a/3/ea344283b6fa26e4a02989dd1fb52a51.png)
, kutovima
![\alpha](/media/m/f/c/3/fc35d340e96ae7906bf381cae06e4d59.png)
,
![\beta](/media/m/c/e/f/cef1e3bcf491ef3475085d09fd7d291e.png)
,
![\gamma](/media/m/2/4/a/24aca7af13a8211060a900a49ef999e9.png)
i poluopsegom
![s](/media/m/9/0/8/908014cbadb69e42261a56b450a375b9.png)
vrijedi jednakost
%V0
Dokaži da u trokutu $ABC$ s duljinama stranica $a$, $b$, $c$, kutovima $\alpha$, $\beta$, $\gamma$ i poluopsegom $s$ vrijedi jednakost $$
s^2 = b^2\cos^2\frac{\gamma}2 + c^2\cos^2\frac{\beta}2 + 2bc\cos\frac{\beta}2\cos\frac{\gamma}2\cos\frac{\beta+\gamma}2 \text{.}
$$