What does (cos(2x))^2 equal?

  1. 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! :)
     
  2. jcsd
  3. What is there to solve??? :confused:

    (cos2x)^2 is just an expression.
     
  4. HallsofIvy

    HallsofIvy 40,678
    Staff Emeritus
    Science Advisor

    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.
     
  5. Doesn't (cos(2x))2 = cos2(2x)2 = cos2(4x2) ?
     
  6. Astronuc

    Staff: Mentor

    No. 'Cos' is a particular operation and 2x is the argument. The exponent of 2 operates on cos, not on the argument.

    cos2y = 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).
     
  7. HallsofIvy

    HallsofIvy 40,678
    Staff Emeritus
    Science Advisor

    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).
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?