Question

Найдите значение выражения. 20 баллов!
$sqrt{2}- 2sqrt{2}sin^2frac{15pi }{8}$

Answer 1

Ответ:  1

Объяснение:

$2sin^2x=1-cos2x\\2sin^2{frac{15pi}{8} }=1-cos{frac{30pi}{8} }=1-cos{frac{15pi}{4} }=1-cos{frac{15-8pi}{4}}=1-frac{sqrt{2} }{2} \\sqrt{2}-sqrt{2}cdot (1-frac{sqrt{2} }{2})=sqrt{2}-sqrt{2}+frac{sqrt{2}sqrt{2} }{2}=1$

Answer 2

$sqrt{2}-2sqrt{2}sin^2dfrac{15pi}{8}=sqrt{2}-2sqrt{2}cdot dfrac{1-cos (2cdot frac{15pi}{8})}{2}=sqrt{2}cos dfrac{15pi}{4}=\ \ \ =sqrt{2}cos left(4pi-dfrac{pi}{4}right)=sqrt{2}cos dfrac{pi}{4}=sqrt{2}cdot dfrac{1}{sqrt{2}}=1$