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Q4. If \( tan A \ = \ cot B \) , prove that \( A + B \ = \ 90° \).
Answer :

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

=> \( cot B \ = \ tan(90° - B) \)

∴ \( tan A \ = \ tan(90° - B) \)

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

=> \( A + B \ = \ 90° \)