Question

Найдите значение выражения √128 cos^2 5pi/8- √32

Answer 1

$sqrt{128}cdot cos^2frac{5pi }{8}-sqrt{32}=sqrt{2^7}cdot frac{1+cosfrac{10pi }{8}}{2}-sqrt{2^5}=\\=8sqrt2cdot frac{1+cos(pi +frac{pi}{4})}{2}-4sqrt2=4sqrt2cdot (1+(-cosfrac{pi}{4})-1)=\\=4sqrt2cdot (-frac{sqrt2}{2})=-4\\\star ; ; cos^2alpha =frac{1+cosalpha }{2}; ; ; ;; ; ; cos(pi +alpha )=-cosalpha ; ; star$

Answer 2

$sqrt{128} cos ^{2}  frac{5 pi }{8} - sqrt{32} = sqrt{32} ( sqrt{4} cos ^{2}  frac{5 pi }{8} -1)=sqrt{32} ( 2 cos ^{2}  frac{5 pi }{8} -1)=  \ 
sqrt{32}cos(2* frac{5 pi }{8} )=sqrt{32}cosfrac{5 pi }{4} = sqrt{32} * (-frac{ sqrt{2} }{2} )=-4$