Let's consider all the trig identities, to help us with the problem:
⇒ (look at the attached image for help with that)
After looking at all the trig identity, let's look at the problem given to us:
⇒ cos(θ) = [tex]\frac{5}{13}[/tex]
⇒ we know that sec(θ) = 1 / cos(θ) = 1 / (5/13) = 13/5
Thus: sec(θ) = 13/5, which just so happens to be Choice (D)
Answer: sec(θ) = 13/5 or Choice (D)
Hope that helps!
