Question

Найдите значение выражения √2-√8×sin²*3п/2

Answer 1

$sqrt{2}- sqrt{8}sin^2 (frac{3 pi }{2})=?\\sin frac{3 pi }{2}=-1= textgreater sin^2( frac{3 pi }{2})=(sin frac{3 pi }{2})^2= (-1)^2=1\ sqrt{8}= sqrt{2^2*2}=2 sqrt{2}\\ sqrt{2}- sqrt{8}sin^2 (frac{3 pi }{2})=sqrt{2}- sqrt{8}*1= sqrt{2}-2 sqrt{2} =- sqrt{2}$