How would you express f(x) = cos3(x) in terms of first powers only? Please explain the steps
by first powers do you mean no squares, cubes etc?
If so, then I can't think of a way to do that.
If you meant express in terms of 1x you could do the following
cos 3x = cos(2x+x)
=cos2xcosx - sin2xsinx
=(1-2sin^2 x)cosx - (2sinxcosx)sinx
from here you could go in different directions, but the expression is in terms of sinx and cosx