# This is a difficult problem- Identities

1. Apr 28, 2006

### thunder

Prove this identity:

sin (2 X)
----------------- = 2 sin (X) - 2 sin^2 (X)
sec (X) + tan (X)

How would you do it? It was suggested in another thread that this can't be proved or that there is an error in the problem...but I think it is a hard problem to figure out. Anyeays, the teacher said that it was provable...so I'm really not sure. Seems to be stumping most of us today though. Good luck!!

I'll check back to see who the winner is

2. Apr 28, 2006

### Hurkyl

Staff Emeritus
It's not hard -- the basic algorithm for proving these identities works quite well.

(1) Convert everything into sines and cosines.
(2) Get rid of all fractions. (e.g. simplifying, cross multiplying, ...)
(3) Get everything to have the same angle.

at which point the identity is usually very easy to prove. (It is often already proven at this point! But alas that is not the case here)

Last edited: Apr 28, 2006
3. Apr 28, 2006

### Curious3141

Much as I'd like to be the winner. , this is not a competition, this is homework. It isn't difficult, it took me all of 10 seconds to write it out. So I'll just give you a few hints :

Work on the LHS and make it look like the RHS.

For the numerator of the LHS, use double angle formula.

For the denom., express secant and tangent in terms of sine and cosine.

Simplify the algebra and see what you get. At one point you'll need $$\sin^2x + \cos^2x = 1$$