Final answer:
The Laplace transform of sinh(at)−4cos(at) is a/(s^2-a^2) - 4s/(s^2-a^2).
Step-by-step explanation:
The Laplace transform of sinh(at)−4cos(at) can be found by using the linearity property of the Laplace transform and the known Laplace transforms of sinh(at) and cos(at).
The Laplace transform of sinh(at) is given by a/(s^2-a^2) and the Laplace transform of cos(at) is given by s/(s^2-a^2).
Therefore, the Laplace transform of sinh(at)−4cos(at) is a/(s^2-a^2) - 4s/(s^2-a^2).