Prove that cosh (3x) = 4 * (coshx) ^ 3 + 3 * coshx

Prove that cosh (3x) = 4 * (coshx) ^ 3 + 3 * coshx

Cosh (3x) = cosh (2x + x) = cosh (2x) * cosh (x) + Sinh (2x) * Sinh (x) = (2 * cosh ^ 2 (x) - 1) * cosh (x) + 2 * Sinh (x) * cosh (x)) * Sinh (x) = 2 * cosh ^ 3 (x) - cosh (x) + (2 * cosh ^ 2 (x) - 2) * cosh (x)) = 4 * (COSH x) ^ 3-3 * COSH