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