Verify the following identity: Help!

[aem23]

I continue to get stuck during this problem. If anyone could help, that would be superb.

Here goes:

Verify the identity:

cscxsin3x - secxcos3x = 2

 

[Loren]

Change csc x to 1/sin x and sec x to 1/cosx. Add the terms on the left side. You should get...
\(\displaystyle \frac{\cos x\sin 3x - \sin x\cos 3x}{\sin x \cos x}\)

Now, do some jockeying until it simplifies to \(\displaystyle \frac{\sin(3x-x)}{\sin x \cos x}\)

I leave the rest to you.