If angle A and Angle B are acute angles such that Cos A equal to cos B then show that angle A equal to Angle B.
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ANSWER:-
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 )
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