Math, asked by muskanmalik8397, 11 months ago


angle A and angle B are acute angles such that cos A = cos B, then show that angleA= angle B.

Answers

Answered by riyabakshi123
2

Step-by-step explanation:

Please see the photo Hope it helps you

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Answered by Disha976
0

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!

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