Proving TRIG Identity

[Anna]

I'm Trying to prove the following Identity:
(Sin2x / Sinx) - (Cos2x / Cosx) = Secx
I changed that to:
Sinx Cos2X - Sin2x Cosx
----------------------------
Sinx Cosx

But I don't know how to simply it further. (I know the Secx = 1 / Cosx so I'm trying to make the Left side the same.)

 

[galactus]

Use the identities:

\(\displaystyle sin(2x)=2sin(x)cos(x)\) and

\(\displaystyle cos(2x)=2cos^{2}(x)-1\)

Make those subs and it should fall into place.