Let's prove that for all c, In (cosh(x)) > - In(2) For all c ec Number By adding to both sides of this inequality Since the right hand side of this equation is positive, we can take the natural logarithm; In(e te " ) > By the definition of cosh (a) : In(2 cosh(I)) Hence by log laws In (cosh(z)) = QED Note: the Maple syntax for ed and In(a) are exp (x) and In (x) respectively