Hi David,
What a loaded question!!
Some things you need to consider are:
Is the singer going to be stationary?
Next to or far away from the piano?
Are audience sightlines an issue?
How important is the piano sound? Are you looking for just a reference or do you need a nice stereo recording?
What is your budget?
If the piano and singer are stationary in the center of the stage and sightlines are NOT and issue, google “ORTF recording”. There are many articles online on how to do this technique. You will record singer and piano in one stereo field. Your AT4050 alone won’t cut it, though.
If your piano is off to one side of the stage and the singer is going to be moving around the stage, I would put a wireless mic on her, and run the cable up the back of her neck, and hide the mic head just inside her hairline, and in the center of her forehead. That way, no matter where she goes or how she turns her head, her sound will be consistent.
Then I would take your 4050 and put it on a boom stand, and stick it about 5 ft. in front of the piano at piano level.
If that piano micing technique is a little too bush league, (and it is), then renting a couple of 414’s and spacing them inside the piano about 1/3 of the way in from each side and 2 feet above the strings is a better alternative. If you want better than that let us know, there are other techniques that are more time consuming and expensive to pull off.
If you go this route, consider having another mic (stereo?) on the lip of the stage or a little ways into the audience to capture some ambience because she will sound a little dry.
Let us know if you have any more questions.
I am sure everyone is going to chime in with their favorite techniques that will differ from these, just pick the ones that fit your budget and sound right to you. There is more than one way to skin a cat.
Peter