Question

If ∆ABC and ∆PQR if angle A and angle P are acte angles such that tanA=tanP then prove that the angle A = angle P?​

Answer 1

Answer:

Solution

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From the figure,

tanA=ACBC

tanB=BCAC

Given

tanA=tanB

ACBC=BCAC

AC2=BC2

AC=BC

In Triangle ABC, AC=BC. Hence , ABC is a scalene triangle.

If two sides of a triangle are equal, then the angles opposite to the sides are always equal.

Therefore, ∠A=∠B