[tex] \sqrt{32} cos^2 \frac{ \pi }{8} - \sqrt{8} [/tex]

[tex]\sqrt{32} cos^2 \frac{ \pi }{8} - \sqrt{8} \\\sqrt8(\sqrt4cos^2\frac{\pi}{8}-1)=2\sqrt2(2cos^2\frac{\pi}{8}-1)=2\sqrt2cos(2*\frac{\pi}{8})=\\2\sqrt2cos\frac{\pi}{4}=2\sqrt2*\frac{\sqrt2}{2}=2\\\\cos2x=2cos^2x-1[/tex]