Hello, all!

I need to prove the following identity:

$\displaystyle \frac{cos(x-y)}{sin(x-y)} = \frac{1 + tan\hspace{5 pt}x\hspace{5 pt}tan\hspace{5 pt}y}{tan\hspace{5 pt}x + tan\hspace{5 pt}y}$

I am able to prove that the left side of the equation is equal to:

$\displaystyle \frac{1 + tan\hspace{5 pt}x\hspace{5 pt}tan\hspace{5 pt}y}{tan\hspace{5 pt} x - tan\hspace{5 pt}y}$

The obvious difference between what I am able to prove and what the identity actually says is the difference in sign between tan x and tan y in the denominator.

I'll be happy to explain how I arrived at my proof, but I'm hoping it should be pretty straight forward to understand.

So my question is this:

Is there some way to prove this identity, or is this a false identity (perhaps a misprint in the text I'm reading)?

Thank you!