Question

5. If angleA and angleB are acute angles
such that cos A = cos B, then show
that angleA= angleB.
​

Answer 1

given

cos A= cosB

A= cos inverse cosB

A=B

so

angle A=angle B

hence prove

Answer 2

We are given that,

$\qquad \rm {• cos \: A = cos \: B }$

________

We have to show,

$\qquad \rm {• ∠A = ∠B }$

________

Construction,

$\dag$ Draw a triangle ABC where C = 90°.

__________

Solution

We know,

$\qquad \rm {• cos \: A = cos \: B }$

$\implies { \rm \dfrac{B}{H} = \dfrac{B}{H} }$

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

$\implies \rm{ AC \times \cancel {AB} = BC \times \cancel {AB} }$

$\rm {\implies AC = BC }$

Now , we know that if two sides of triangle are equal than it is isosceles triangle and we also know that in isosceles triangle, if two opposite sides are equal than their angle will also be equal.

$\implies { \rm \angle A= \angle B }$

Thus, prooved!