cosh'(x) = sinh(x)
sinh'(x) = cosh(x)
cosh(0) = 1
sinh(0) = 0
(a) Prove that for all x, cosh(x) + sinh(x) = e^x.
(b) Prove that for all x, cosh(x) - sinh(x) = e^{-x}.
(c) Prove the following equalities:
cosh(x) = (e^x + e^{-x})/2
sinh(x) = (e^x - e^{-x})/2
(d) For each of cosh(x) and sinh(x), determine if the function is even, odd, or neither, and prove your claim.
(e) For all b ∈ R, prove that (cosh(x) + sinh(x))^b = cosh(bx) + sinh(bx).
