Question

if angle A and angle B are acute angles such that cosA=cosB , then show that angle A= angle B.​

Answer 1

A=45

B=45

so A=B

I hope it will be answer of your question

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

Some Identity to be used here

$\large{\sf\:{cos\theta=\dfrac{Base}{Hypotenuse}}}}$

In Right Angle Triangle :-

$\tt{\rightarrow cosA=\dfrac{AC}{AB}}$

Also :-

$\tt{\rightarrow cosB=\dfrac{BC}{AB}}$

cosA = cosB (Already given in question)

AC = BC

$\tt{\rightarrow\dfrac{AC}{AB}=\dfrac{BC}{AB}}$

Therefore

In ∆ABC :-

AC = BC

★As we know that the angle which is opposite to equal sides are always equal

★Hence :-

∠A = ∠B