Simplification

Hello,

I am having trouble trying to simplify the following expression;

cos^2(x) - tan^2(x) / 1 + tan^2(x)

Help is much appreciated,

Dranalion

Hi Dranalion

You can try to apply identity :

Given the identity,
sec^2(x) = 1 + tan^2(x)

This makes the identity:

cos^2(x) - tan^2(x)/sec^2(x)


Which is:

cos^2(x) - tan^2(x)/(1/cos^2(x))

How do I further simplify this expression?

Quote:

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Originally Posted by songoku

Hi Dranalion

You can try to apply identity :

---

After you apply this you have:



Hope this helps
-Chad

Sorry, the identity is actually the divided term to be subtracted from cos^2(x), as in:

cos^2(x) - [ tan^2(x)/(1/cos^2(x)) ]

Then you just have this:



-Chad

Thanks!

If you have cos^2(x) - sin^2(x), can you use the identity:
sin^2(x) + cos^2(x) = 1 to somehow simplify this further? Or is this as far as it can be simplified?

Careful, we have:

The identity reads:

Ours is not the same. In ours, we have the difference, so we cannot use that identity here.

Hi Dranalion