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°.
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