# Proving Identities

• Oct 6th 2009, 01:26 PM
oryxncrake
Proving Identities
How do I prove the following identity?

cosx (secx - cscx) = 1 - cotx

For the left side, I am at:

cosx (1/cosx - 1/sinx)

Am I anywhere near being right so far? Or is there an easier way to simplify the identity?
• Oct 6th 2009, 01:41 PM
pickslides
Its a really good start

$\displaystyle \cos(x) \left(\frac{1}{\cos(x)} - \frac{1}{\sin(x)}\right)$

now expanding $\displaystyle \cos(x)$ in you get

$\displaystyle \frac{\cos(x)}{\cos(x)} - \frac{\cos(x)}{\sin(x)}$

Spoiler:

and simplifying

$\displaystyle 1- \frac{1}{\tan(x)}$

$\displaystyle 1- \cot(x)$
• Oct 6th 2009, 01:52 PM
oryxncrake
Quote:

Originally Posted by pickslides
Its a really good start

$\displaystyle \cos(x) \left(\frac{1}{\cos(x)} - \frac{1}{\sin(x)}\right)$

now expanding $\displaystyle \cos(x)$ in you get

$\displaystyle \frac{\cos(x)}{\cos(x)} - \frac{\cos(x)}{\sin(x)}$

Spoiler:

and simplifying

$\displaystyle 1- \frac{1}{\tan(x)}$

$\displaystyle 1- \cot(x)$

Thanks so much. I just get so confused with the simplifying!
• Nov 4th 2009, 02:49 AM
meyanne