Question

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

Answer 1

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