Ta cÓ:
a^2+b^2=c^2+4R^2
\Leftrightarrow 4R^2\sin^2A+4R^2\sin^2B=4R^2\sin^2C+4R^2
\Leftrightarrow \sin^2A+\sin^2B=\sin^2C+1
\Leftrightarrow 2\sin^2A-1+2\sin^2B-1=2\sin^2C
\Leftrightarrow -\cos2A-\cos2B=2\sin^2C
\Leftrightarrow -\cos(A-B)\cos(A+B)=\sin^2C
\Rightarrow \tan^2C=\frac{-\cos(A-B)\cos(A+B)}{\cos^2C}
=\frac{-\cos(A-B)}{\cos(A+B)}
=\frac{\sin A\sin B+\cos A\cos B}{\sin A\sin B-\cos A\cos B}
=\frac{\tan A\tan B+1}{\tan A\tan B-1}