If $∠ A$ and $∠ B$ are acute angles such that $cos A = cos B$ then prove that $∠ A = ∠ B$ .

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Solution

According to the question:-
Let $cos A = \frac{s i d e a d j a c e n t A}{H y p o t e n u s e}$
$\frac{A C}{A B}$
Similarly,
$cos B = \frac{s i d e a d j a c e n t B}{H y p o t e n u s e}$
$= \frac{B C}{A B}$
Given that
$cos A = cosB$
$\frac{A C}{A B} = \frac{B C}{A B}$
$A C = B C$
In triangle,
angles opposite equal side are equal
$∠ B = ∠ A$

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