Find the Laplace Transform of sint cost | L{cost sint}

The Laplace transform of sint cost is equal to 1/(s²+4). Here we will learn how to find the Laplace of sint cost.

The Laplace of sint cost is denoted by L{sint cost}, and its formula is given by

$\boxed{L\{\sin t \cos t\} = \dfrac{1}{s^2+4}}$.

Laplace of sint cost

Answer: The Laplace of sint cost is 1/(s²+4).

Explanation:

Using the trigonometric identity sin2θ = 2sinθ cosθ, the given function can be written as follows:

sint cost

= $\dfrac{1}{2}$ 2 sint cost

= $\dfrac{1}{2}$ sin2t

So the Laplace transform of the product sint cost will be

L{sint cost} = L{$\dfrac{1}{2}$ sin2t}

⇒ L{sint cost} = $\dfrac{1}{2}$ L{sin2t}

⇒ L{sint cost} = $\dfrac{1}{2} \times \dfrac{2}{s^2+2^2}$ as we know L{sinat} = a/(s²+a²).

⇒ L{sint cost} = $\dfrac{1}{s^2+4}$.

So the Laplace transform of sint cost is equal to 1/(s²+4).

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