# Express in terms of cosine.

• December 16th 2008, 09:16 AM
Intrusion
Express in terms of cosine.
I need some help with this one...

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

• December 16th 2008, 09:23 AM
Moo
Hello,
Quote:

Originally Posted by Intrusion
I need some help with this one...

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

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