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yuSmady upapade samAnAdhikaraNe sthAniny api madhyamaH

युष्मद्युपपदे समानाधिकरणे स्थानिन्यपि मध्यमः ONPANINI 14105

A verb gets second person endings when its referent is second person, even if it does not appear in the sentece.

Example. In —

tvam pacasi त्वं पचसि "you are cooking"

The pac पच् + /laT verb **pacasi पचसि got /sip because it links to its doer **tvam त्वम्, which is a second person noun.

Why do we say "even if that noun has been deleted"?

In the sentence —

pacasi पचसि "you are cooking"

there is no /tvam, but we say **pacasi पचसि anyway.

So, I guess that saying tvam pacasi त्वं पचसि is in some sense better than saying just pacasi पचसि?

No — the /pANinIya just says that things are right or wrong, does not make subtle distinctions about what is better than what. Bot pacasi पचसि and tvam pacasi त्वं पचसि are right according to /pANini, and you are alwasy free to choose.

However, usage and custom tell us that just pacasi पचसि is better than tvam pacasi त्वं पचसि about 99% of the time.

Can you give some examples of the other 1%?

Sure. You use the extra word for contrastive emphasis —

tvam pacasi ahan tu pave
त्वम्पचसि अहं तु पवे
"you do the cooking and I do the cleaning, oki?"

and to fill up a —

gaccha tvam bhrAtarau gRhya kiSkindhAM rAma;lakSmaNau |
गच्छ त्वं भ्रातरौ गृह्य किष्किन्धां रामॱलक्ष्मणौ ।
"grab you the brothers rAma राम and lakSmaNa लक्ष्मण and take them to kiSkindhA किष्किन्धा"

just gaccha गच्छ with no **tvam त्वम् would have worked in prose.

Is that gRhya grammatical?

No, it should be **gRhItvA . That's the epics for you.

But why didn't vAlmIki just say gRhItvA bhrAtarau gaccha kiSkindhAM rAma;lakSmaNau | ?

Hey, he lived thousands of years before /pANini. Saying gRhya was not frowned upon back then.