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**Ronald****Guest**

During class I faced a problem- cos^4(x)+cos^2(x)=1,my friend told me that x=acos(sqrt(phi-1)).when I checked it using calculator,it was correct.how is phi involved in this,please explain.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,362

Hi Ronald;

You make the substitution y = cos(x) and then solve.

Another substitution, u=y^2.

Now it is easy.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**Ronald****Guest**

I get acos(sqrt(sqrt(1.25)-1)),so?

**Ronald****Guest**

Sorry it is (sqrt(sqrt(1.25)-.5))

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,362

Please check your work I am not getting that. For one root I am getting.

That is what you wanted to show.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**Ronald****Guest**

Wait a minute,1/2(sqrt(5)-1) and sqrt(1.25)-.5 is same!

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,362

Yes, it is the same but there is no reason to convert to decimal. You should avoid unnecessary simplifications. The way it is done in post #5 is fine.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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