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If ∠A and ∠p are acute angles such that tan A = tan P, then show that ∠A = ∠P.

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In a right angled triangle APQ,

tan A = \(\frac{PQ}{AQ}\) and tan p = \(\frac{AQ}{PQ}\)

 ∵  tan A = tan P

\(\frac{PQ}{AQ}\) = \(\frac{AQ}{PQ}\)

∴ PQ = AQ

∠P = ∠A = 45°

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