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

1. Apr 11, 2007

justine411

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. Apr 11, 2007

neutrino

What is there to solve???

(cos2x)^2 is just an expression.

3. Apr 11, 2007

HallsofIvy

Staff Emeritus
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.

4. Apr 12, 2007

Rhythmer

Doesn't (cos(2x))2 = cos2(2x)2 = cos2(4x2) ?

5. Apr 12, 2007

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).

6. Apr 12, 2007

HallsofIvy

Staff Emeritus
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).