Algebra and Trigonometry 10th Edition

The trigonometric Identity is verified. $cos^2β-sin^2β=2~cos^2β-1$
$sin^2β+cos^2β=1~~$ (Pythagoren Identity) $cos^2β-1=-sin^2β$ Now: $cos^2β-sin^2β=cos^2β+cos^2β-1=2~cos^2β-1$