Prove given identities

**hachm361** · November 9th 2012, 04:42 PM

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

Please help, I don't know where to start or how to complete this.

**richard1234** · November 9th 2012, 04:50 PM

Rewrite everything in terms of sine and cosine.

**amillionwinters** · November 9th 2012, 04:56 PM

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

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

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

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

**Soroban** · November 9th 2012, 05:45 PM

Hello, hachm361!

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

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

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

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

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

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