Question

if tan x is equal 5 / 12 then find sec x

Answer 1

Viewed as a right angled triangle 
tan(x)=512
can be thought of as the ratio of opposite to adjacent sides in a triangle with sides 5,12 and 13 (where 13 is derived from the Pythagorean Theorem)

So

sec(x)=13/12

Answer 2

We know that 1+( tanx)^2 =( secx)^2
So 1 + (5/12)^2 = (secx)^2
Secx =√(1+25/144)
Secx = √169/144
Secx = 13/12