If you want to check the display value, https://stackoverflow.com/a/1189281/5622596 already posted the answer.
However if instead of checking whether an element has a style of style="display:none"
you want to know if that element is visible. Then use .is(":visible")
For example:
$('#idDetails').is(":visible");
This will be true
if it is visible & false
if it is not.