Trigonometry Expansion: Expanding cos(8x) Using sin(2⋅x) or cos(2x)

[Panphobia]

Homework Statement

We know that sin(2⋅x)=2⋅sin(x)⋅cos(x)and cos(2x)=cos^2(x)−sin^2(x). Use the appropriate formula to expand cos(8x) in terms of one of these two formulas.

Homework Equations

sin(2⋅x)=2⋅sin(x)⋅cos(x)
cos(2x)=cos^2(x)−sin^2(x)

The Attempt at a Solution

I am not looking for help with the solution, I just want to know what the question is asking me to do. Is it asking me to sub cos(8x) into these equations like cos(8x) = cos^2(4x) - sin^2(4x)? If not what is it asking me to do?

Thank You!

 

[Mark44]

Homework Statement

We know that sin(2⋅x)=2⋅sin(x)⋅cos(x)and cos(2x)=cos^2(x)−sin^2(x). Use the appropriate formula to expand cos(8x) in terms of one of these two formulas.

Homework Equations

sin(2⋅x)=2⋅sin(x)⋅cos(x)
cos(2x)=cos^2(x)−sin^2(x)

The Attempt at a Solution

I am not looking for help with the solution, I just want to know what the question is asking me to do. Is it asking me to sub cos(8x) into these equations like cos(8x) = cos^2(4x) - sin^2(4x)?

Yes. Now do the same sort of thing on the cos(4x) and sin(4x) terms.

Note that the notation cos²(4x) means [cos(4x)]², and similar for sin²(4x).

If not what is it asking me to do?

Thank You!