Question

6) LA and LB are acute angle such that
Cos A = cos B Then show that LA = LB​

Answer 1

Step-by-step explanation:

Given:-

angle A and angle B are acute angle such that

Cos A = cos B

To find:-

Show that LA = LB

Solution:-

Consider a right angled triangle ABC and right angle at angle C.

angle A and angle B are acute angles

AB is the hypotenuse

Now

Cos A = Adjacent side to angle A/ Hypotenuse

Cos A = AC/AB-------(1)

Cos B = Adjacent side to angle B/ Hypotenuse

Cos B = BC/ AB-------(2)

Given that

Cos A = Cos B

From (1)&(2)

=> AC/AB = BC/AB

=> AC = BC

We know that

In a triangle ,the angles opposite to equal sides are equal.

angle opposite to AC = angle B

angle opposite to BC = angle A

=> angle A = angle B

Hence, Proved .

Answer:-

In a triangle ,angle A and angle B are acute angle such that Cos A = cos B then angle A = angle B

Used formula:-

• Cos A = Adjacent side to angle A / Hypotenuse