Es un problema de trigonometria Me pueden ayudar por favor?

<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctext%7BDe%20la%20ley%20de%20cosenos%20se%20tiene%20%3A%7D%20%5C%5C%5B4pt%5D%0Aa%5E2%3Db%5E2%2Bc%5E2-2bc%5Ccos%20A%5C%5C%5B4pt%5D%0A%5CRightarrow%20%5C%20a%5E2-b%5E2-c%5E2%3D-2bc%5Ccos%20A%20%5C%20...%20%5C%20%28i%29%20%5C%5C%5B4pt%5D%0A%5Ctext%7BPor%20dato%20%3A%20%20%7D%20a%5E2-b%5E2-c%5E2%3D%5Cfrac%7B2bc%7D%7B3%7D%20%20%5C%5C%5B4pt%5D%0A%5Ctext%7BSe%20reemplaza%20en%20la%20ecuaci%5C%27%7Bo%7Dn%20%7D%20%28i%29%20%20%5C%5C%5B4pt%5D%0A%5Cfrac%7B2bc%7D%7B3%7D%20%3D-2bc%5Ccos%20A%20%5C%20%5CRightarrow%20%5C%20%5Ccos%20A%3D-%5Cfrac%7B1%7D%7B3%7D%20%5C%5C%5B4pt%5D%0A%5Ctext%7BPor%20identidades%20de%20%5C%27%7Ba%7Dngulo%20mitad%20se%20tiene%20%3A%20%7D%5C%5C%5B4pt%5D%0A%5Ctan%5Cleft%28%5Cfrac%7BA%7D%7B2%7D%20%5Cright%29%3D%5Cpm%20%5Csqrt%7B%5Cfrac%7B1-%5Ccos%20A%7D%7B1%2B%5Ccos%20A%7D%7D%20%5C%5C%5B4pt%5D%0A%0A" />

<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctext%7BEn%20un%20tri%5C%27%7Ba%7Dngulo%20el%20%5C%27%7Ba%7Dngulo%20mitad%20es%20siempre%20%20agudo%7D%20%5C%5C%5B4pt%5D%0A%5Ctext%7Bentonces%20la%20tangente%20de%20la%20mitad%20ser%5C%27%7Ba%7D%20positiva%20%2C%20reemplazando%20%3A%7D%20%5C%5C%5B4pt%5D%0A%5Ctan%5Cleft%28%5Cfrac%7BA%7D%7B2%7D%20%5Cright%29%3D%20%5Csqrt%7B%5Cfrac%7B1-%28-%5Cfrac%7B1%7D%7B3%7D%29%7D%7B1%2B%28-%5Cfrac%7B1%7D%7B3%7D%29%7D%7D%20%3D%5Csqrt%7B%5Cfrac%7B1%2B%5Cfrac%7B1%7D%7B3%7D%7D%7B1-%5Cfrac%7B1%7D%7B3%7D%7D%7D%3D%5Csqrt%7B%5Cfrac%7B4%2F3%7D%7B2%2F3%7D%7D%3D%5Csqrt%7B2%7D%20%20%5C%5C%5B4pt%5D%0A%0A%5Cdisplaystyle%20%5Ctext%7B%20Por%20lo%20tanto%20%3A%20%7D%20%5Ctan%5Cleft%28%5Cfrac%7BA%7D%7B2%7D%20%5Cright%29%3D%5Csqrt%7B2%7D%20%0A" />.