Verify the identity $\cos^2x-\sin^2x = 2\cos^2x-1$ I am having problems understanding how to verify this identity. I am quite sure that it is to be solved using the Pythagorean identities but, alas, I'm not seeing what might otherwise be obvious. 
I need to verify the identity 
$$\cos^2x-\sin^2x = 2\cos^2x-1$$
Thank you for your help.

Remember that $sin^2(x) = 1 - cos^2(x)$.
Then $cos^2x - sin^2x = ?$
