Simplifying Trig Identity: cos^2x - cos^4x = cos^2x sin^2x

[tornzaer]

Homework Statement

cos^2x - cos^4x = cos^2x sin^2x

Homework Equations

N/A

The Attempt at a Solution

L.S. = cos^2x -(cos^2x)(cos^2x)
= cos^2x -cos^2x(cos^2x)

I'm stuck here. Am I doing something wrong during the first step? Thanks for your help.

 

[nanoWatt]

What are you trying to solve for, x? Or are you trying to simplify it?

 

[tornzaer]

It's trig identity. Trying to make the left side look like the right side.

 

[rocomath]

manipulate the right side, it's easier ... you want it all in terms of cosine

 

[HallsofIvy]

Homework Statement

cos^2x - cos^4x = cos^2x sin^2x

Homework Equations

N/A

The Attempt at a Solution

L.S. = cos^2x -(cos^2x)(cos^2x)
= cos^2x -cos^2x(cos^2x)

I'm stuck here. Am I doing something wrong during the first step? Thanks for your help.

Didn't we just do one like this? cos^2(x)- cos^4(x)= cos^2(x)- cos^2(x) cos^(x)= cos^2(x)(1- cos^2(x)). Does that help?

 

[tornzaer]

Didn't we just do one like this? cos^2(x)- cos^4(x)= cos^2(x)- cos^2(x) cos^(x)= cos^2(x)(1- cos^2(x)). Does that help?

Sort of but it's too cluttered.

If I try to manipulate the right side, I get this:

= (cos^2x)(sin^2x)
= (cos^2x)(1-cos^2x)

After that, I don't know how to make the cos^4 on the left side.

 

[rocomath]

= (cos^2x)(sin^2x)
= (cos^2x)(1-cos^2x)

foil ...

 

[tornzaer]

foil ...

God... how did I miss that. Thanks a lot.

I'm just really tense. Got a huge test tomorrow and trying to cram it all. A week for stuff in a day isn't a good idea... Thanks again!