Answer
$${\text{0}}{\text{.894427191}}$$
Work Step by Step
$$\eqalign{
& \cos \left( {{{\tan }^{ - 1}}0.5} \right) \cr
& {\text{Find using a calculator, set the degree ,mode}} \cr
& \left. 1 \right){\text{ Press cos}} \cr
& \left. 2 \right){\text{ Press shift}} \cr
& \left. 3 \right){\text{ Press tan}} \cr
& \left. 4 \right){\text{ Type in the keys 0}}{\text{.5}} \cr
& \left. 5 \right){\text{ Press = }} \cr
& {\text{The result is 0}}{\text{.894427191}} \cr} $$