Proving Trig Problem: sec (2x) - 1 = sin^2 x / 2 sec (2x)

[Sixlets]

I'm stuck :/ I have to prove the following:
sec (2x) - 1 = sin^2 x
____________
2 sec (2x)

Unfortunately, I don't know any terms that are equal to sec (2x). Any help would be awesome!

 

[Eldar]

$$sec(2x)=\frac{1}{cos(2x)}=\frac{1}{cos^2x-sin^2x}$$

Also you can change the denominator by substituting in for $$cos^2x$$ or $$sin^2x$$.

 

[QuarkCharmer]

I think I would start with the left side of the eq. and use the double angle identity to get it in terms of sin/cos.

 

[Sixlets]

I'll try that again. I kept getting way off track, but I probably just got confused with all the fractions haha. Thanks everyone!