Step 1: Identify the protein. Keratin is the primary structural fibrous protein that makes up hair, feathers, horns, claws, and hooves.
Step 2: Determine the secondary structure. In mammals, the keratin in hair is \(\alpha\)-keratin. The secondary structure of \(\alpha\)-keratin is the \(\alpha\)-helix. (Beta-sheets are characteristic of \(\beta\)-keratins found in reptiles and birds).
Step 3: Identify the cross-linking. The strength and insolubility of hair keratin come from extensive cross-linking between the \(\alpha\)-helical protein chains. These cross-links are primarily disulfide bonds, formed between cysteine amino acid residues.
Step 4: Evaluate the options. Option (1) correctly states both key features: an alpha-helix structure and cross-linking by disulfide bonds. The other options are incorrect regarding either the structure or the cross-linking.