Inverse Fourier transforming a function

I have the below function of q and t that I need to take the inverse fourier transform of to get a function of t:

exp(-i*q.*t)*((sin(q)./q))./(sin(q)+i*rho*c*cos(q))

I don't have the symbolic toolbox and am scratching my head over what to do. Thanks!

[Anton Semechko]

you dont need the symbolic toolbox for this, just use paper and pencil