Whether you’re writing a cover letter, grant application, or professional report, “etc.” has no place in formal communication.
Picture some of history’s and popular culture’s most enduring quotes with the addition of “etc.”:
“That’s one small step for man, etc.”
“I’ll get you, my pretty, etc.”
If you’re still tempted to use “etc.” in your writing, imagine replacing it with, “I couldn’t be bothered to complete this.”
The one exception is the case in which you are writing to an audience that you are absolutely sure will understand what you mean, in which case you may choose to shorten a long list with “etc.”