Verified answer

     cos²x – sin²x = 2cos²x – 1 ... use identity: sin²x = 1 – cos²x

 cos²x – (1 – cos²x) = 2cos²x – 1

  cos²x – 1 + cos²x = 2cos²x – 1

     2cos²x – 1 = 2cos²x – 1 ... TRUE

There's an identity that says cos^2(x) + sin^2(x) = 1. You'll need to know this.

Change everything into cosine.. Which means you have to convert sin^(x) into terms of cosine. So now you mess around with your identity to figure this out:

Plug it in. DON'T FORGET THE PARENTHESIS!!!

Cos^2(x) - {1 - cos^2(x)} = 2cos^2(x) - 1

Distribute the negative.

Cos^2(x) - 1 + cos^2(x) = 2 cos^2(x) - 1

Add up the cos^2(x)'s on the left side.

2cos^2(x) - 1 = 2cos^2(x) - 1

I'd eliminate the ones, but as long as you proved it I think you're good.