1. ## Prove given identities

SecA TanA
----- - ----- = 1
CosA Cot A

2. ## Re: Prove given identities

Rewrite everything in terms of sine and cosine.

3. ## Re: Prove given identities

Think of the pythagorean identity $\displaystyle tan^2(x) + 1 = sec^2(x)$

See how it can be re-arranged to look like $\displaystyle sec^2(x) - tan^2(x) = 1$

Now, how are $\displaystyle \frac{sec(x)}{cos(x)}$ and $\displaystyle sec^2(x)$ related?

How are $\displaystyle \frac{tan(x)}{cot(x)}$ and $\displaystyle tan^2(x)$ related?

4. ## Re: Prove given identities

Hello, hachm361!

$\displaystyle \text{Prove: }\:\frac{\sec A}{\cos A} - \frac{\tan A}{\cot A} \:=\:1$

Do you know any basic identities . . . like these?

. . $\displaystyle \cos A \,=\,\frac{1}{\sec A} \qquad \cot A \,=\,\frac{1}{\tan A} \qquad \sec^2\!A - \tan^2\!A \:=\:1$

If you don't, you need more help than we can offer.

We have: .$\displaystyle \frac{\sec A}{\cos A} - \frac{\tan A}{\cot A} \;=\;\frac{\sec A}{\frac{1}{\sec A}} - \frac{\tan A}{\frac{1}{\tan A}} \;=\;\sec^2\!A - \tan^2\!A \;=\;1$