1.

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

Answer»

In a right angled triangle ABC,

cos A = \(\frac{AC}{AB}\) and cos B = \(\frac{BC}{AB}\)

 ∵ cos A = cos B

\(\frac{AC}{AB}\) = \(\frac{BC}{AB}\)

∴ AC = BC

We have, opposite sides of equal angles are equal. 

Therefore, In a right angled triangle ABC

∠A = ∠B = 45°



Discussion

No Comment Found