"You are sad."
Translation:तुम दुखी हो।
Earlier I had translated this as आप दुख हैं, but this time I decided to be a bit more casual with तुम दुख हो only to be typo corrected with तुम दुखी हो. Funny! And since the question passed (only a typo) I couldn't report what seemed to be an error, or at least an optional translation.
But then, in the same lesson this sentence राज बहुत दुखी है uses दुखी, a feminine verb, for a masculine object राज. Am I missing some subtle grammatical point here? Is तुम दुखी हो used even when speaking to a man?
I was expecting 'sad' to be ग़म, (having seen kabhi khushi kabhi gam) which now checking Wiktionary tells me means sorrow/grief/mourning. But it also gives duukhi as a synonym, and its page also includes sorrow and grief as meanings.
So is there any subtle difference in meaning between ग़म और दूखी, or just straight synonyms?