I want to get across in my cover letter that I'm a person who will dig in and do whatever I have to do to find the answer to a complicated problem at work. I want to let the hiring manager know that I don't stop until I have an answer and that he or she will be happy to hire me. Any suggestions?
Thanks for writing! Let's think about the "you'll be happy" part of your message. Let's back all the way out of the familiar cover-letter paradigm, and think about what it means to say to another person "You will be happy to meet me" (much less to hire me). When we ponder this message for a few seconds, we can see the problem with it.
We don't know what makes another person happy. Only that person knows. Different things make different people happy.
We don't want to say "You will be happy to meet me/hire me." We push the reader away with a message like that. Rather, we want to say "I'm not sure - you are the expert, obviously - but I have the impression that you may be dealing with the notorious Scaly Red Norwegian dragon, a species I've had occasion to slay on several occasions. If I am correct, it may be good for us to talk."
We don't want to start analyzing our skills and talents in a cover letter. We're not believable at that early stage. When we tell a story about having slain the same dragon the hiring manager is facing, we're instantly credible -- or, more accurately, we give the hiring manager the (appropriate) authority to assess our credibility via the story we provide.
"You will be happy to hire me" is overreaching. That's a pushaway message.
"Hearing about your national distribution deal with Whole Foods, I wondered whether you'd be in need of more hands on deck in your Inventory Control organization" is closer to the mark. Here we say "I wouldn't presume to know the inside scoop, but the externally-available facts suggest that you might have Red Scaly flying around your castle walls right now." When we add "At Angry Chocolates, I built an inventory-control framework that kept us in stock at 14,000 retailers more than 94% of the time, supporting 40% year-over-year sales growth" we aren't standing back and saying "I do this and I do that, and I have these tendencies, proclivities and gifts," we're showing up with the proof, rather than a suspect self-assessment.
Try it! Let us know if you need help spotting the employer's pain and/or settling on a relevant dragon-slaying story.
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