Question

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

Answer 1

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