Question

If angle A and angle B are acute angles such that cos A = cos B, then show that angle A = angle B.


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Answer 1

Answer:

According to the question:-

Let cosA=

Hypotenuse

sideadjacentA

AB

AC

Similarly,

cosB=

Hypotenuse

sideadjacentB

=

AB

BC

Given that

cosA=cosB

AB

AC

=

AB

BC

AC=BC

In triangle,

angles opposite equal side are equal

∠B=∠A

Step-by-step explanation:

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Answer 2

Question:

If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B.

Given:

• Let ABC be right angles triangle.
• ∠A and ∠B are acute angles
• cos A = cos B

To prove : ∠A = ∠B

Proof :

In right angled triangle ABC

cos A = $\dfrac{Side~adjacent~to~∠A}{Hypotenuse} = \dfrac {AC}{AB}$

cos B = $\dfrac{Side~adjacent~to~∠B}{Hypotenuse} =\dfrac {BC}{AB}$

Since, we know that cos A = cos B

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

AC=AB

Hence, ∠A = ∠B (angles opposite to equal sides of triangle)