Express in terms of cosine.

**Intrusion** · December 16th 2008, 09:16 AM

I need some help with this one...

$(1 - \tan^2\Theta)(\sec^2\Theta)$

Thanks in advance.

**Moo** · December 16th 2008, 09:23 AM

Hello,

Originally Posted by Intrusion

I need some help with this one...

$(1 - \tan^2\Theta)(\sec^2\Theta)$

Thanks in advance.

Note that $1+\tan^2 \theta=\sec^2 \theta$

So $1-\tan^2 \theta=2-\sec^2 \theta$

Hence $(1-\tan^2 \theta)(\sec^2 \theta)=2 \sec^2 \theta-\sec^4 \theta=\frac{2}{\cos^2 \theta}-\frac{1}{\cos^4 \theta}$

**Intrusion** · December 16th 2008, 09:38 AM

Thank you, you're amazing

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