If \( tan A \ = \ cot B \) , prove that \( A + B \ = \ 90° \).

Given, \( tan A \ = \ cot B \)
We know that, \( cot \theta \ = \ tan(90° – \theta) \)

=> \( cot B \ = \ tan(90° - B) \)

\( tan A \ = \ tan(90° - B) \)

=> \( (90° – A) \ = \ B \) [\(\because \) (90° – A) and B are both acute angles ]

=> \( A + B \ = \ 90° \)