Question

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

Answer 1

Answer:

removing cos on both sides u can get

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!