Question

sinα*cosα , если sinα-cosα=√2

Answer 1

$Sin \alpha -Cos \alpha = \sqrt{2}\\\\(Sin \alpha -Cos \alpha ) ^{2} =( \sqrt{2} ) ^{2}\\\\Sin ^{2} \alpha -2Sin \alpha Cos \alpha +Cos ^{2} \alpha =2 \\\\1-2Sin \alpha Cos \alpha =2\\\\2Sin \alpha Cos \alpha =-1\\\\Sin \alpha Cos \alpha =- \frac{1}{2}$