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    if angle a and angle b are acute angles such that cos a is equal to cos b then show that angle a is equal to angle b

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    If angle A and angle B are acute angles such that cosA=cosB, then show that angleA=angle B.

    If angle A and angle B are acute angles such that cosA=cosB, then show that angleA=angle B.

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    If angle A and angle B are acute angles such that cosA=cosB, then show that angleA=angle B.

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    If angle A and angle B are acute angles such that cosA=cosB, then show that angleA=angle B.

    Open in App Solution

    Suggest Corrections 17 SIMILAR QUESTIONS

    Q.

    If ∠A and ∠B are acute angles such that cos A = cos B, then show that

    ∠A = ∠B.

    Q. If ∠A and ∠P are acute angles such that tan A = tan P, then show that ∠A = ∠P.Q. If

    ∠ A and ∠ B

    are acute angles such that

    cos A = cos B then prove that ∠ A = ∠ B .

    Q. Question 6

    If ∠ A and ∠

    B are acute angles such that cos A = cos B, then show that

    ∠ A = ∠ B.

    Q. In triangle ABC and triangle XYZ if angle A and angle X are acute angles such that cosA=cosX then show that angle A=angle X

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    स्रोत : byjus.com

    If A and B are acute angles such that cos A = cos B then prove that A = B .

    Click here👆to get an answer to your question ✍️ If A and B are acute angles such that cos A = cos B then prove that A = B .

    Question

    If ∠A and ∠B are acute angles such that cosA=cosB then prove that ∠A=∠B.

    Medium Open in App Solution Verified by Toppr

    According to the question:-

    Let cosA= Hypotenuse sideadjacentA ​ AB AC ​ Similarly, cosB= Hypotenuse sideadjacentB ​ = AB BC ​ Given that cosA=cosB AB AC ​ = AB BC ​ AC=BC In triangle,

    angles opposite equal side are equal

    ∠B=∠A

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    स्रोत : www.toppr.com

    If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B

    If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B. Using cos A and cos B, we can find ratio of the length of two sides of the right-angled triangle with respective angles.

    If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B

    Solution:

    Using the basic trigonometric ratios, we can solve this problem.

    In the right-angled triangle ABC as shown below, ∠A and ∠B are acute angles and ∠C is right angle.

    cos A = side adjacent to ∠A / hypotenuse = AC/AB

    cos B = side adjacent to ∠B / hypotenuse = BC/AB

    Given that cos A = cos B

    Therefore, AC/AB = BC/AB

    AC = BC

    Hence, ∠A = ∠B (angles opposite to equal sides of a triangle are equal.)

    Let's look into an alternative approach to solve the question.

    Let us consider a triangle ABC in which CO ⊥ AB.

    It is given that cos A = cos B

    AO/AC = BO/BC AO/BO = AC/BC

    Let AO/BO = AC/BC = k

    AO = k × BO ...(i) AC = k × BC ...(ii)

    By applying Pythagoras theorem in ΔCAO and ΔCBO, we get

    AC2 = AO2 + CO2 (from ΔCAO)

    CO2 = AC2 - AO2 ...(iii)

    BC2 = BO2 + CO2 (from ΔCBO)

    CO2 = BC2 - BO2 ...(iv)

    From equation (iii) and equation (iv), we get

    AC2 - AO2 = BC2 - BO2

    (kBC)2 - (kBO)2 = BC2 - BO2 [From equation (i) and (ii)]

    k2BC2 - k2BO2 = BC2 - BO2

    k2 (BC2 - BO2) = BC2 - BO2

    k2 = (BC2 - BO2)/(BC2 - BO2) = 1

    k = 1

    Putting this value in equation (ii) we obtain,

    AC = BC

    Thus, ∠A = ∠B (angles opposite to equal sides of triangle are equal.)

    ☛ Check: NCERT Solutions Class 10 Maths Chapter 8Video Solution:

    If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B

    Maths NCERT Solutions Class 10  Chapter 8 Exercise 8.1 Question 6

    Summary:

    If ∠A and ∠B are acute angles such that cos A = cos B we have proved that ∠A = ∠B since AC = BC and angles opposite to equal sides of a triangle are equal.

    ☛ Related Questions:

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    If 3 cot A = 4, check whether (1 - tan2 A) / (1 + tan2 A) = cos2 A - sin2 A or not.

    In the triangle ABC right-angled at B, if tan A = 1/√3 find the value of:(i) sin A cos C + cos A sin C(ii) cos A cos C - sin A sin C

    In ΔPQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

    स्रोत : www.cuemath.com

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