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प्रश्न
If ∠A and ∠B are acute angles such that sin A = Sin B prove that ∠A = ∠B.
उत्तर
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)
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