Given triangle PQR,

PR = 13cm

PQ = 12cm

According to Pythagorean theorem,

In a right- angled triangle, the squares of the hypotenuse side is equal to the sum of the squares of the other two sides.

PR² = QR² + PQ²

Substitute the values of PR and PQ

13² = QR²+12²

169 = QR²+144

Therefore, QR² = 169−144

QR² = 25

QR = √25 = 5

Therefore, the side QR = 5 cm

To find tan P – cot R:

tan (P) = Opposite side /Adjacent side

= QR/PQ = 5/12

Since cot function is the reciprocal of the tan function, the ratio of cot function becomes,

Cot (R) = Adjacent side/Opposite side = QR/PQ = 5/12

tan (P) – cot (R) = 5/12 – 5/12 = 0

Therefore, tan(P) – cot(R) = 0