Question

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

Answer 1

A and P are acute angle tan A = tan P

Let us consider right angled triangle ACP,

We know `tan theta = "opposite side"/"adjacent side"`

`tan A = (PC)/(AC)`

`tan P = (AC)/(PC)`

tanA =tan P   ....(Given)

`(PC)/(AC) = (AC)/(PC)`

`(PC)^2 = (AC)^2`

PC = AC   [∵ Angle opposite to equal sides are equal]

∠P = ∠A