In this paper, we will rediscover formulas for hyperbolic functions of multiple angles. Such formulas do exist in mathematical handbooks, but the versions that we will present are somewhat different from them. As a by product of these formulas, we will also obtain several formulas for trigonometric functions of multiple angles. The last section of the paper carries interesting and novel results: The formulas for hyperbolic functions and trigonometric functions of multiple angles imply some remarkable identities involving Binomial Coefficients. Most results in the paper were obtained with the help from the computer algebra system Mathematica.