Question

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

Answer 1

In ΔABC, ∠𝐶 = 90°

Tan A = `(BC)/(AC)` and 

Tan B = `(AC)/(BC)`

As, tan 𝐴 = tan 𝐵

`⇒ (BC)/(AC) = (AC)/(BC)`

`⇒ BC^2 = AC^2`

⇒ BC=AC

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