Explanation:

5cosθ + 12sinθ = 13;
(5/13) * cosθ + (12/13) * sinθ = 1;
Suppose that the angle formed in the figure is ∅.
sin∅.cosθ+cos∅.sinθ= 1;
sin(θ + ∅)= sin90;
θ + ∅ = 90;
θ =90- ∅;
cos θ= cos(90- ∅);
cos θ=sin∅= 5/13;