The formal Tamil translation for "How are you?" in a professional email context is:
**"เฎจเฏเฎเฏเฎเฎณเฏ เฎเฎชเฏเฎชเฎเฎฟ เฎเฎฐเฏเฎเฏเฎเฎฟเฎฑเฏเฎฐเฏเฎเฎณเฏ?"**
*(Nฤซแน
kaแธท eppaแนญi irukkiแนฤซrkaแธท?)*
This is the polite and respectful form suitable for formal communication.
For additional context, you could also use:
**"เฎเฎเฏเฎเฎณเฏ เฎจเฎฒเฎฎเฏ เฎเฎชเฏเฎชเฎเฎฟ เฎเฎณเฏเฎณเฎคเฏ?"**
*(Uแน
kaแธท nalam eppaแนญi uแธทแธทadhu?)*
*(Literally: "How is your well-being?")*
Both are appropriate for professional correspondence.