Solution:

By using Pythagoras theorem in △PQR, we have

PR² = PQ² + QR²

Putting the length of given side PR and PQ in the above equation,

13² = 12² + QR²

QR² = 13² – 12²

QR² = 169 – 144

QR² = 25

QR = √25 = 5

By definition,

tan P = Perpendicular side opposite to P/ Base side adjacent to angle P

tan P = QR/PQ

tan P = 5/12 ………. (1)

And,

cot R= Base/Perpendicular

cot R= QR/PQ

cot R= 5/12 …. (2)

When comparing equation (1) and (2), we can see that R.H.S of both the equation is equal.

Therefore, L.H.S of both equations should also be equal.

∴ tan P = cot R

Yes, tan P = cot R = 5/12