Trig Identity

  • Thread starter tornzaer
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  • #1
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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.
 

Answers and Replies

  • #2
88
2
What are you trying to solve for, x? Or are you trying to simplify it?
 
  • #3
77
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It's trig identity. Trying to make the left side look like the right side.
 
  • #4
1,753
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manipulate the right side, it's easier ... you want it all in terms of cosine
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
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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?
 
Last edited by a moderator:
  • #6
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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.
 
  • #8
77
0
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!
 

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