Urgent help with verifying trigonmetric identities

1/secxtanx = cscx - sinx

I've tried some ways and every way I do this, I keep ending up in a dead end. It's not only just this problem, there's more I have trouble with. So, if anyone out there has some useful tips and strategies for verifying these trigonometric identities. It would be much appreciated. Thank You.

So anyway, 1/secxtanx = cscx - sinx. Here's what I attempted to do:

1/secxtanx = cscx - sinx

1/(1/cosx)(sinx/cosx) = cscx-sinx

cosx cosx/sinx = cscx-sinx

Here's where I run into trouble. What do I do? Where did I go wrong? I've spent a long time trying to figure this out and I'd love some help right now. So if anyone could help me, thanks.