I have to find the laplace transform of cos(at) * cos(bt) and express it as a ratio of two polynomials. I converted both of the cosines into exponentials, and took the laplace transform of those. I think I'm getting confused on the complex side of things. I get a few things like e^(jt(a+b)), and e^(-jt(a+b)) so I use Euler's formula and get some cosines and jsines. So how do you find the laplace transform of say jsin(t(-a-b)). Shouldn't it just be j*s / (s^2 + (-a-b)^2)? Except this does not yield the correct answer. Maybe I'm converting all of the transforms to one fraction incorrectly...?