Looking on the internet deeply has found these results:

at the cost of is the most popular phrase on the web.

at the expense of 152,100,000 results on the web	at the cost of 1295,000,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
She became your focus at the expense of your own ambition. Congratulations, you have been given a luxury penthouse at the expense of the British taxpayer. A small elite lives in great luxury at the expense of the poor population. All these developments are taking place at the expense of Cypriot consumers and are clearly illegal. But not at the expense of our cause. But not at the expense of your health. I don't want to be stylish at the expense of comfort. However, this change in behaviour should not be at the expense of consumer protection.	This option renders a better image at the cost of increased calculation. Once students' rights come at the cost of others, it is my job to intervene. But it can't be at the cost of the other things we are trying to achieve here. However, this must not come at the cost of social uncertainty. financed public investment will produce a short Free movement within the European Union must not be implemented at the cost of the EU's erecting barriers against the surrounding world. Instead, debt They won the battle at the cost of many lives.

at the expense of

152,100,000 results on the web

at the cost of

1295,000,000 results on the web

More popular!

She became your focus at the expense of your own ambition.
Congratulations, you have been given a luxury penthouse at the expense of the British taxpayer.
A small elite lives in great luxury at the expense of the poor population.
All these developments are taking place at the expense of Cypriot consumers and are clearly illegal.
But not at the expense of our cause.
But not at the expense of your health.
I don't want to be stylish at the expense of comfort.
However, this change in behaviour should not be at the expense of consumer protection.

This option renders a better image at the cost of increased calculation.
Once students' rights come at the cost of others, it is my job to intervene.
But it can't be at the cost of the other things we are trying to achieve here.
However, this must not come at the cost of social uncertainty.
financed public investment will produce a short
Free movement within the European Union must not be implemented at the cost of the EU's erecting barriers against the surrounding world.
Instead, debt
They won the battle at the cost of many lives.