To solve this problem, we need to identify which compounds are synthesized from the amino acid Tryptophan.$\newline$Let's analyze each option:$\newline \bullet$Option 1: Melatonin and serotonin.$\newline$ - Tryptophan is a precursor for serotonin, a neurotransmitter.$\newline$ - Serotonin can be further converted into melatonin, a hormone that regulates sleep.$\newline$ - Therefore, Tryptophan is indeed a precursor for both melatonin and serotonin.$\newline \bullet$Option 2: Thyroxine and triiodothyronine.$\newline$ - These are thyroid hormones synthesized from tyrosine, not tryptophan.$\newline$ - Therefore, this option is incorrect.$\newline \bullet$Option 3: Estrogen and progesterone.$\newline$ - These are steroid hormones derived from cholesterol, not tryptophan.$\newline$ - Therefore, this option is incorrect.$\newline \bullet$Option 4: Cortisol and cortisone.$\newline$ - These are also steroid hormones derived from cholesterol, not tryptophan.$\newline$ - Therefore, this option is incorrect.$\newline$Based on the analysis, the correct answer is Option 1: Melatonin and serotonin.