Question

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

Answer 1

Given:

To show:

Consider two right angled triangles ABC and PQR such that

Therefore we have,

and

Since it is given that

Therefore,

Now by interchanging position of AB and QR by cross multiplication

We get,

Let (say) …… (1)

Now by cross multiplication

and …… (2)

Now by using Pythagoras theorem in triangles ABC and PQR

We have,

and

Therefore

and

Now

Now using equation (2)

We get,

Now by taking common

We get,

Therefore,

Now gets cancelled

Therefore,

…… (3)

From (1) and (3)

Therefore,

Hence,