<em>A. He tells the Cyclops his name even though it risks the lives of his men.</em>
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<u>Explanation:</u>
The detail from the Odyssey which best shows that Odysseus can be vain is that there are unnecessary risks which are taken by him endangering his crew members so that he taunt the cyclops. The state of Ithaca is also entailed in the details of Odyssey. There are certain risks which are taken by him and goes in vain as they are of no use to him and in the plot construction and his actions.