The question may be ambiguous:
(1) sin(x), sin(2x), 2cos(x)sin(x); or
(2) sin(x), sin²(x), 2cos(x)sin(x)?
In case (1), sin(2x)=2cos(x)sin(x) by trig identity, so 2nd and 3rd terms are essentially identical.
My guess is:
sin(x), sin(2x), 2cos(x)sin(x), sin(3x), sin(2x)cos(x)+cos(2x)sin(x).
There are a number of variations for the 5th term:
a) sin(2x)cos(x)+cos(2x)sin(x)
b) cos(x)sin(2x)+cos(2x)sin(x)
c) sin(2x)cos(x)+sin(x)cos(2x)
d) cos(x)sin(2x)+sin(x)cos(2x)
e) cos(2x)sin(x)+sin(2x)cos(x)
f) cos(2x)sin(x)+cos(x)sin(2x)
g) sin(x)cos(2x)+sin(2x)cos(x)
h) sin(x)cos(2x)+cos(x)sin(2x)
to name a few.