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∠A and ∠B are acute angles such that tanA=tanB, then prove that ∠A=∠B.

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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


1 Answer

  1. 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).

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