An important and exam oriented question from trigonometric ratios in which we have given ∠A and ∠B are acute angles such that tanA=tanB, we have to prove that ∠A=∠B.
RS Aggarwal, Class 10, chapter 10, question no 31
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Consider ΔABC to be a right angled triangle
angle C = 90 degree
tan A = BC/AC and
tan B = AC/BC
Given: tan A = tan B
So, BC/AC = AC/BC
BC^2 = AC^2
BC = AC
Which implies, ∠ A = ∠ B (using triangle opposite and equal angles property).