. de Moivre's theorem is used to express cos no and sin ne in terms of cos and sin when n is an integer. The equivalent for the hyperbolic sine and cosine is not quite as easy to write down. However, write cosh in terms of e and e- and square both sides of the equation. Hence find cosh 20 in terms of cosh 0. Further, can you think of a quick way of determining a simple expression for sinh 20 in terms of sinh and cosh ? Also, find an expression for sinh 30 in terms of powers of sinh 0, and an expression for cosh 30 in terms of powers of cosh 0.