Question

$sqrt{32} cos^2 frac{ pi }{8} - sqrt{8}$

Answer 1

$sqrt{32} cos^2 frac{ pi }{8} - sqrt{8} \sqrt8(sqrt4cos^2frac{pi}{8}-1)=2sqrt2(2cos^2frac{pi}{8}-1)=2sqrt2cos(2*frac{pi}{8})=\2sqrt2cosfrac{pi}{4}=2sqrt2*frac{sqrt2}{2}=2\\cos2x=2cos^2x-1$