If ∠A and ∠P are acute angle such that tan A = tan p, then show th

1.	If ∠A and ∠P are acute angle such that tan A = tan p, then show that ∠A = ∠P.
Answer» 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°

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

Answer»

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°