trigonometric equation help?

Lets start with the left hand side.

The bottom looks like a difference of squares factorization- so lets multiply it out

LHS = (cosX(sinX+cosX))/[1-(Sin(x))^2]

(because the middle terms sin(x) - sin(x) cancel)

Now, one of the fundamental identities is (cosX)^2 + (sinX)^2 = 1. You will hopefully know this (if you don't, its relatively simple to derive it from Pythagoras- its a used ALL the time) Simple rearrangement tells us that (cosX)^2 = 1 - (sinX)^2 <-- this is now what we have on the botttom, so we can substitute:

LHS = cosX(sinX+cosX)/(cosX)^2

Now the cosX's can cancel, we use tanX = sinX/cosX and we arrive at the result on the RHS.

The trick here is expanding the bottom- when stuck, look for ways to get to know identities, expand brackets, factor etc. You may sometimes find it helpful to work back the RHS- this isn't one of those cases but they do come up.