1. The problem statement, all variables and given/known data (cos2x)^2 2. Relevant equations 3. The attempt at a solution I'm not sure if it is cos^2(2x) or cos^2(4x) or what. Should I use an identity to simplify it to make it easier to solve? Please help! :)
In what sense is (cos(2x))^{2} a "problem"? What do you want to do with it? I will say that (cos(2x))^{2} means: First calculate 2x, then find cosine of that and finally square that result. Notice that it is still 2x, not 4x. The fact that ^{2} is outside the parentheses means that it only applies to the final result.
No. 'Cos' is a particular operation and 2x is the argument. The exponent of 2 operates on cos, not on the argument. cos^{2}y = cos y * cos y. There are also particular trigonometric identites with which one should be familiar, i.e. cos (x+y) and sin (x+y).
You still haven't told us what the problem was! Was it to write (cos(2x))^2 in terms of sin(x) and cos(x)? I would simply be inclined to write (cos(2x))^2 as cos^2(2x).