Question

If angle a and angle b are acute angles such that cos a=cosb then show that angle a=angle b

Answer 1

your answer is in the image.

Answer 2

We are given that,

$\qquad \rm {• cos \: A = cos \: B }$

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We have to show,

$\qquad \rm {• ∠A = ∠B }$

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Construction,

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

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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!