Let us assume a right angled triangle ABC, right angled at B

sec θ =13/12 = Hypotenuse/Adjacent side = AC/AB

Let AC be 13k and AB will be 12k

Where, k is a positive real number.

According to the Pythagoras theorem,

AC²= AB² + BC²

Substitute the value of AB and AC

(13k)² = (12k)² + BC²

169k² = 144k² + BC²

169k² = 144k² + BC²

BC² = 169k² – 144k²

BC²= 25k²

BC = 5k

Now, substitute the corresponding values in all other trigonometric ratios

Sin θ = Opposite Side/Hypotenuse = BC/AC = 5/13

Cos θ = Adjacent Side/Hypotenuse = AB/AC = 12/13

tan θ = Opposite Side/Adjacent Side = BC/AB = 5/12

Cosec θ = Hypotenuse/Opposite Side = AC/BC = 13/5

cot θ = Adjacent Side/Opposite Side = AB/BC = 12/5