Why Do Fundamental Trig Identities Confuse Me?

[WastingBody]

I just don't get this stuff. I've been trying on my own with the book. Also, is there a better way to post this?

Homework Statement

tanx 1 + secx
_________ + _________ = 2csc x
1 + secx tanx
I need to prove that this side equals the other.

Homework Equations

http://users.rcn.com/mwhitney.massed/trigresources/trig-reference.html
^^The reference I was using.

The Attempt at a Solution

tanx(tanx) 1 + secx(1 + secx)
_________ + _________ = 2csc x
1 + secx(tanx) tanx(1 + secx)
tan2 x 1 + 2secx + sec2x
________________ + _________________
1 + secx(tanx) (tanx)1 + secx
tan2x + 1 + 2secx + sec2x
_________________________
1 + cos 1/x(tanx)sec2x + 2cos 1/x + sec2x
_________________________
1 + cos 1/x(tanx)

This is as far as I get before I get lost.

 

[Integral]

First look at https://www.physicsforums.com/showthread.php?t=8997"thread to learn how to use LaTex. With that you can do this:

\frac { \tan x } { 1 + \sec x} + \frac {1 + \sec x} {\tan x} = 2 \csc x

Now, try multipling the top and bottom of the first term on the left by 1 - \sec x

BTW: Just click on my equations to see what I typed to produce them.