Question

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

Answer 1

$y = sqrt{128*cos^2frac{5pi}8} - sqrt{32}\cos^2frac{5pi}8 = cos^2112.5 = cos^2frac{225}2 = frac{1+cos(pi+45)}2 = frac{1-cos45}2 = frac{1-frac{sqrt2}2}2 = frac{2-sqrt2}4\y = sqrt{128*frac{2-sqrt2}4} - sqrt{32} = sqrt{32(2-sqrt2)} - sqrt{32} = sqrt{32}(sqrt{2-sqrt2}- 1)$