Laplace transform of multiplication of two terms with different arguments

Question

What is the Laplace Transform of the product of two functions with different arguments?
The function is: $\mathcal{L}( \sin({3 t}) \cos({5 t}) )$

Answer 1

HINT:

Use Werner Formula , $$2\sin A\cos B=\sin(A+B)+\sin(A-B)$$

and we know, $$L\{\sin(at)\}=\dfrac a{s^2+a^2}$$