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Answer :
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 ]
=> \( A + B \ = \ 90° \)