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If Angle a and Angle B Are Acute Angles Such that Cos a = Cos B, Then Show that Angle a = Angle B. - Mathematics

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

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Solution

∠A and ∠B are acute angles

Cos A = cos B S.T ∠A = ∠B

Let us consider right angled triangle ACB.

We have `cos A = "adjacent side"/"Hypotenuse"`

`= (AC)/(AB)`

`cos B = (BC)/(AB)`

cos A = cos B

`(AC)/(AB) = (BC)/(AB)`

AC = BC

∠A = ∠B

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 10 Trigonometric Ratios
Exercise 10.1 | Q 33 | Page 25
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