Apply Theorem 2 to verify that {cos kt} = s/(s 2 + k 2 ). THEOREM

Apply Theorem 2 to verify that ℒ {cos kt} = s/(s² + k²).

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THEOREM 2 Transforms of Periodic Functions Let f(t) be periodic with period p and piecewise continuous for t≥ 0. Then the transform F(s) = L{f(t)} exists for s> 0 and is given by F(s) = = 1 - P₁ [ ² e-²₁ 1- e-ps e-st f(t) dt. (6)