For the next two (02) items that follow : Let \(4(A+B) = \pi\).
What is \((\cot A-1)(\cot B-1)\) equal to?
\(2\)
From \(A+B=\pi/4\), \(\tan A+\tan B=1-\tan A\tan B\). Writing \((\cot A-1)(\cot B-1)=\cot A\cot B-\cot A-\cot B+1\) in terms of \(\tan A,\tan B\) and simplifying using this relation gives the value \(2\).
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