Question

If in a triangle, $\angle A$ and $\angle B$ are acute angles such that $\cos A=\cos B$, then, is $\angle A=\angle B$?

• A. Yes
• B. No
• C. Ambiguous
• D. Data insufficient

Answer 1

Correct option is A. Yes.

Let $△ACB$ be a right angled triangle at point $C$.

Now, ATQ,

$\cos A=\cos B$

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

$\Rightarrow AC=BC$

$\Rightarrow \angle ABC=\angle BAC$ [As angles opposite to equal sides are equal]

Hence, $\angle A=\angle B$