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Question
If ∠A and ∠B are acute angles such that tan A= Tan B then prove that ∠A = ∠B
Solution
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)
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