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

  1. Apr 11, 2007 #1
    1. The problem statement, all variables and given/known data


    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. Apr 11, 2007 #2
    What is there to solve??? :confused:

    (cos2x)^2 is just an expression.
  4. Apr 11, 2007 #3


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    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. Apr 12, 2007 #4
    Doesn't (cos(2x))2 = cos2(2x)2 = cos2(4x2) ?
  6. Apr 12, 2007 #5


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    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. Apr 12, 2007 #6


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    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).
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