If tan A = cot B where A and B are acute angles, prove that A + B = 90°

Given that, A and B are acute angles.

⇒ A < 90° & B < 90°

So, using trigonometric identity, we can say

tan (90° - B) = cot B [∵, tan (90° - θ) = cot θ]

Replace cot B of RHS by tan (90° - B) in the given question.

tan A = cot B

⇒ tan A = tan (90° - B)

Now, comparing the degrees from the above, we get

A = 90° - B

⇒ A + B = 90°

Hence, proved that A + B = 90°.