Question

6. If angle A and angle B are acute angles such that cos A = cos B, then show that
angleA = angleB.
(short trick)​

Answer 1

${\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox{\fbox {\purple{your-answer-is.... }}}}}}}}}}}$

hope it helps u plz make me brainliest plz don't forget about it and thank you for your question friend

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!