Question

if <A and <B are acute angles such that COS A=COS B. Then show that ANGLE A=ANGLE B​

Answer 1

Step-by-step explanation:

In triangle ABC ,

Cos A = opposite side / hypo.

= AC / AB -1

Cos B = adjacent side / hypo.

= BC / AB -2

We gave cos A = cos B

Thus by 1 and 2,

AC / AB = BC / AB

Thus

AC . AB = BC . AB

AC = BC

thus AC and BC are two sides of triangle ABC

Thus angle A = angle B

( angles opposite to equal sides are equal )

This is the answer .

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Answer 2

Answer:

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Step-by-step explanation:

cosa = Cosb

cos^-1(cosa)=b

[cos^-1(cosa)= a]

a=b

hence proved