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The phrase "a tough task to" is correct and usable in written English.
It can be used when describing a challenging assignment or responsibility that someone has to undertake.
Example: "Completing the project on time is a tough task to manage with so many unexpected obstacles."
Alternatives: "a challenging task to" or "a difficult task to".
Exact(54)
The Swiss champions face a tough task to score the two goals needed.
But it still faces a tough task to restore its advantage over other banks.
It was a tough task to ask him off the bench.
With Bayern Munich also in Group F, Lille face a tough task to qualify.
But still, it's such a tough task to ask to win all four Grand Slams in a year.
So Purcell, when he set out to write Freeman's biography, found it a tough task to get at the facts.
Similar(6)
Yet so much has changed geographically and demographically — not to mention in cyberspace — that it is a designer's tough task to make the references relevant.
Whoever ends up owning Barnes & Noble faces a tough task: adapt to the Brave New World, or be consigned to the History section.
Ferulic acid (FA) extraction is a tough task due to its linkage with the hemicellulose, which is difficult to break.
Ensuring cooperation between network nodes may be a tough task due to the misbehavior of network nodes.
Spain coach Julen Lopetegui believes his side - who begin their title defence against Russia before facing Germany and Holland in Group B - have a tough task ahead to retain their trophy.
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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