How do I behave around the taken woman I am attracted to?

I am attracted to a co-worker who is in a long-term relationship and I asked her out before I knew about her relationship. We haven't gone out anymore after she told me about it. I respect her relationship and only expressed my interest in a very subtle and polite way. However, I feel I am a bit dishonest since I talk to her on a weekly basis without expressing my feelings, but at the same time expressing them wouldn't change anything.

How do I behave around the taken woman I am attracted to?
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