# Homework Help: Help w/ quad angle identity

1. Jan 11, 2012

### physicsgeek54

1. The problem statement, all variables and given/known data
Simplify: cos(4θ)

2. Relevant equations
cos(2θ)=2cos^2(θ)-1
sin(2θ)=2sinθcosθ

3. The attempt at a solution
First, I broke it into cos(2θ+2θ). Then I expanded it and got cos(2θ)cos(2θ)-sin(2θ)sin(2θ). I then expanded that and got (4cos^4(θ)-4cos^2(θ)+1)-(4sin^2(θ)+4sin(θ)cos(θ)+cos^2). I was supposed to get 8cos^4(θ)-8cos^2(θ)+1. I see that I'm off but I don't know where I went wrong.

2. Jan 11, 2012

### Staff: Mentor

the term (4sin^2(θ)+4sin(θ)cos(θ)+cos^2) isn't right for sin^2(2x) = (2sin(x)cos(x))^2 = 4 sin^2(x)cos^2(x)

a simpler derivation would be:

cos(4x) = 2 cos^2(2x) - 1 right?

next we look at the cos(2x) factor: cos(2x) = 2cos^2(x) -1

and plug back into the 2cos^2(2x) - 1

Last edited: Jan 11, 2012
3. Jan 11, 2012

### physicsgeek54

Oh, thanks for catching my mistake. I think I can figure it out now but I don't see how you got from cos(4x) to 2 cos^2(2x)-1.