1. Trig proof for sec^2

I have a proof in my trig book, that I am completely stumped on! I'm sure I am missing something easy, but just can't seem to get there.

sec^2(x)=(sec(2x))(2-sec^2(x))

Any hints?
Thanks!

2. Originally Posted by tshenura

Any hints?
What do you know $\displaystyle \sec^2 x$ being equal to?

Table of Trigonometric Identities

3. Use the relation, $\displaystyle \sec(2x) = (1+(\tan(x))^{2})/(1-(\tan(x))^{2})$, and simplify.