Question

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

Answer 1

${\huge{\pink{\underline{\underline{\purple{\mathbb{\bold{\mathcal{AnSwEr..}}}}}}}}}$

${\large{\blue{\bold{\underline{Given:-}}}}}$

▪︎ CosA = CosB.

▪︎ Let the third angle of triangle be C.

${\large{\blue{\bold{\underline{To\:Prove:-}}}}}$

▪︎ Angle A = Angle B.

${\large{\blue{\bold{\underline{Proof:-}}}}}$

▪︎ We know that,

=》 Cos theta = Base/Hypotenuse {B/H}..

=》 B/H = B1/H.

=》 AC/AB = BC/AB.

=》 AC = BC.

=》 Angle A = Angle B

{Angle opposite to equal sides}

HENCE PROVED.

Hope this will help you if it HELPS then plz mark my answer as BRAINLIEST.

And remember to always keep a smile on face:D

$<marquee>✌✌THANKS✌✌</marquee>$

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!