Wtf, trigonometry.

hai guise. :3
This problem makes absolutely no sense to me;

Rewrite the product as a sum or difference:
sin(8t) sin(4t)

>>2
Or use Euler's formula (or just look it up) to get:
\sin (a) \sin (b)=-\frac{1}{4} \left(e^{i
   a}-e^{-i a}\right) \left(e^{i b}-e^{-i
   b}\right)=\frac{1}{4} \left(-e^{-i
   (a-b)}+e^{i (a-b)}+e^{-i (a+b)}-e^{i
   (a+b)}\right)=\frac{1}{2} (\cos
   (a-b)-\cos (a+b))
So \sin (8t) \sin (4t) becomes \frac{1}{2} (\cos
   (4t)-\cos (12t))