Question

найдите значение выражения ....

Answer 1

$sqrt{32}-sqrt{128}sin^2frac{9pi}{8}=[, sin(frac{9pi}{8})=sin(pi +frac{pi}{8})=-sinfrac{pi}{8}, ]=\\=sqrt{2^5}-sqrt{2^7}sin^2frac{pi}{8}=[, sin^2 alpha =frac{1-cos2 alpha }{2}; to ; sin^2frac{pi}{8}=frac{1-cosfrac{pi}{4}}{2}, ]=\\=sqrt{2^4cdot 2}-sqrt{2^6cdot 2}cdot frac{1-cosfrac{pi}{4}}{2}=2^2sqrt2-2^3sqrt3cdot frac{1-frac{sqrt2}{2}}{2}=\\=4sqrt2-4sqrt2cdot (1-frac{sqrt2}{2})=4sqrt2-4sqrt2+frac{4sqrt2cdot sqrt2}{2}=4$