Laplace Transform for a trig function

Question

Help me finding the Laplace Transform using trig identities for: t sin(2t) sin(5t)

this is what I've got so far:$\frac{1}{4i}[(s-7i)^{-2} + (s+7i)^{-2} - (s-3i)^{-2} - (s+3i)^{-2}]$

Answer 1

Try with that:

$$sin(2t)sin(5t)=\frac{1}{2}[cos(3t)-cos(7t)]$$

• From: $sin(\alpha)sin(\beta)=\frac{1}{2}[cos(\alpha-\beta)-cos(\alpha+\beta)]$

• After you can use this property: $\mathscr{L}[tf(t)]=-\frac{dF(s)}{ds}$