[tex](1+\cot A)(1+\cot B)=1\Leftrightarrow \cot A+ \cot B =1-\cot A.\cot B[/tex]
Ta có: [tex]\cot (A+B) =\frac{\cot A. \cot B -1}{\cot A + \cot B}=\frac{\cot A. \cot B -1}{1- \cot A . \cot B}=-1\Rightarrow A+B= 135^{\circ} \Rightarrow C=45^{\circ}[/tex]