Question

If L {f (t)} = F (s),

Prove that (1) L {cosh at f (t)} = 1/2[F(s - a) + F(s + a)]

(2) L {sin h at f (t)} = 1/2[F(s - a) - F(s + a)]

Answer 1

(1) Consider L {cosh at f(t)} = L{[(e^at + e^-at)/2] f(t)}