8. The hyperbolic cosine and hyperbolic sine functions are defined by the following equa- tions cosh (x) = (ex te ) sinh(x) = =(ex - e-"). (a) Prove that d a d.x -(cosh(x) ) = sinh(x) and (sinh(x) ) = cosh(x) dx (b) Prove the identity er = cosh(x) + sinh(x). (c) Show that 2k+1 cosh(x) = (2k)! and sinh(x) = > K=0 k=0 (2k + 1)! and that each of these Maclaurin series has interval of convergence I = (-0o, co)