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.

we have $\cos(x)^2-\sin(x)^2=\cos(x)^2-(1-\cos(x)^2)=2\cos(x)^2-1$ since
$\sin(x)^2+\cos(x)^2=1$
