Q4. If $$tan A \ = \ cot B$$ , prove that $$A + B \ = \ 90°$$.
Given, $$tan A \ = \ cot B$$
We know that, $$cot \theta \ = \ tan(90° – \theta)$$
=> $$cot B \ = \ tan(90° - B)$$
∴ $$tan A \ = \ tan(90° - B)$$
=> $$(90° – A) \ = \ B$$    [∵ (90° – A) and B are both acute angles ]
=> $$A + B \ = \ 90°$$