How Do You Simplify (cos(2x))^2 Using Trigonometric Identities?

[justine411]

Homework Statement

(cos2x)^2

Homework Equations

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! :)

 

[neutrino]

What is there to solve?

(cos2x)^2 is just an expression.

 

[HallsofIvy]

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.

 

[Rhythmer]

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.

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

 

[Astronuc]

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

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).

 

[HallsofIvy]

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).