Question

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

Solution

Given: …… (1) To show: is as shown in figure below Now since ……from (1) Therefore Now observe that denominator of above equality is same that is AB Hence only when Therefore …… (2) We know that when two sides of a triangle are equal, then angle opposite to the sides are also equal. Therefore from equation (2) We can say that Angle opposite to side AC = Angle opposite to side BC Therefore, Hence, MathematicsRD Sharma (2014)Standard X

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