Problem 04 | First Shifting Property of Laplace Transform

$\mathcal{L}(\sinh at) = \dfrac{a}{s^2 - a^2}$

$\mathcal{L}(\sinh 2t) = \dfrac{2}{s^2 - 2^2}$

$\mathcal{L}(\sinh 2t) = \dfrac{2}{s^2 - 4}$
 

Thus,
$\mathcal{L}(e^t \sinh 2t) = \dfrac{2}{(s - 1)^2 - 4}$

$\mathcal{L}(e^t \sinh 2t) = \dfrac{2}{(s^2 - 2s + 1) - 4}$

$\mathcal{L}(e^t \sinh 2t) = \dfrac{2}{s^2 - 2s - 3}$           answer