# Trigonometry expansion

• 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!

## 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!