Question

If $\angle A$ and $\angle B$ are acute angles such that tan A = tan B , then show that $\angle A=\angle B$

Answer 1

From the figure,

$\tan A=\frac{BC}{AC}$

$\tan B=\frac{AC}{BC}$

Given

$\tan A=\tan B$

$\frac{BC}{AC}=\frac{AC}{BC}$

$A{C}^2=B{C}^2$

$AC=BC$

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, $\angle A=\angle B$