Question

Given that sec θ = 5/4, determine
cot θ + cos θ

Answer 1

here from above figure
cot¤ = 4/3 &cos¤ = 4/5
hence cot¤ + cos¤ = 4/3+4/5 = 32/15
hence the answer to the given question is 32/15

Answer 2

on the basis of Pythagorean theorem..
if sec θ = 5/4 then ,
cot θ =4/3 & cos θ =4/5,
so cot θ + cos θ =4/3+4/5
cot θ + cos θ =32/15