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)

use sin(2a) = 2sin(a)cos(a)

here,
sin(8t) = 2sin(4t)cos(4t)

2sin(4t)cos(4t)sin(4t) = 2((sin(4t))^2)cos(4t)
=2(1-cos^2(4t)cos(4t)
=(2-2cos^2(4t))cos(4t)
=2cos(4t) - 2cos^3(4t)