# If ∠ A and ∠ B are acute angles such that Cos A = Cos B, then show that ∠A = ∠B

To Prove: ∠ A = ∠ B
Given: cos A = cos B
Let there be a right angled triangle ABC, right angled at C.
Now we know that the side opposite to the angle of which we are taking trigonometric ratio is perpendicular, side opposite to right angle is hypotenuse and the side left is base.
So, now let cos of A and B
We know that,

Since for angle A, BC is perpendicular and AC is the base.
Now,

Since for angle B, BC is base and AC is perpendicular.
Given: cos A = cos B
Therefore,
AC = BC
Now, the angles opposite to the equal sides are also equal.
Therefore, ∠A = ∠B
Hence, Proved.

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