[tex]\cos^2A=1-\sin^2A\\
\sin A=\frac{a}{2R}\\
\text{ Deci }\cos^2A=1-\frac{a^2}{4R^2}\\
%\text{ Relatia de demonstrat devine: }\\
\cos^2A+\cos^2B=1-\frac{a^2}{4R^2}+1-\frac{b^2}{4R^2}=2-\frac{a^2+b^2}{4R^2}=\\
=2-\frac{2c^2}{4R^2}=2(1-\frac{c^2}{4R^2})=2\cos^2C
[/tex]
