Question

If ∠A and ∠B are acute angles such that sin A = sin B then prove that ∠A = ∠B.

Answer 1

In ΔABC, ∠𝐶 = 90°

sin A = `(BC)/(AB)`and 

sin B= `(AC)/(AB)`

As, sin 𝐴 = sin 𝐵

`⇒ (BC)/(AB) = (AC)/(AB)`

⇒ BC= AC 

So, ∠𝐴 = ∠𝐵 (𝐴𝑛𝑔𝑙𝑒𝑠 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑒𝑞𝑢𝑎𝑙 𝑠𝑖𝑑𝑒𝑠 𝑎𝑟𝑒 𝑒𝑞𝑢𝑎𝑙)