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Discover LudwigThe phrase "your cooperation" is correct and can be used in written English
You can use it when you need to politely express a request in which someone needs to cooperate with you in order to complete a task. For example, "We will need your cooperation to make this project successful."
Exact(60)
I appreciate your cooperation".
Your cooperation is appreciated".
We appreciate your cooperation.
"We would like your cooperation".
Thanks for your cooperation.
Your cooperation would be greatly appreciated.
Your cooperation will be sincerely regretted.
We will not succeed without your cooperation.
Automatic $50 fine for violation!!!!!! Thank you for your cooperation".
"If I win, I will need your cooperation," he said.
"But I cannot do anything without your cooperation".
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com