The Laplace transform of the function f(t) = cos3 3t

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The Laplace transform of the function
f(t) = cos³ 3t

1. s + 3s
  s² + 81 s² + 9
2. 1 s + 3s
  4 s² + 81 s² + 9
3. 1 s + 3s
  4 s² + 9 s² + 3
4. None of these

Correct Option: B

f(t) = cos³ 3t
We know that
cos 3A = 4 cos³ A – 3 cos A
Therefore,

L{cos³ 3t} =			cos 9t + 3 cos 3t
			4

=	1			s	+ 3	s
	4			s² + 9²		s² + 3²

=	1			s	+	3s
	4			s² + 18		s² + 9