find the equivalent expression to 4sin(t)cos(t)cos(2t)

Question

the correct choice was sin(4t) i dont really understand how to start this or how to expand something like this

Answer 1

4sin(t)cos(t)cos(2t)

=2[2sin(t)cos(t)]cos(2t)

=2[sin(2t)]cos(2t)

=sin(4t)

use the double angle formula for sines:

sin2x =2sinxcosx

use it twice

2sin2xcos2x=sin4x