Q. 64.4( 45 Votes )

If A and X are acute angles such that cos A = cos X then show that A = X.

Answer :

We have


In this ∆AOX,


cos A = cos X


and cos A is given by,


[, ]


Similarly,



AO = OX [clearly, since denominator from either sides cancel each other]


Now, if sides AO and OX of ∆AOX are equal.


Then, A = X [, In a triangle, angles opposite to the equal sides are also equal]


Hence, A = X


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