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

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