Question

1-2/tgα+ctgα,если Cosα-Sinα=-1/3

Answer 1

$1- \frac{2}{tg \alpha _ctg \alpha } =1- \frac{2}{ \frac{sin \alpha }{cos \alpha }+ \frac{cos \alpha }{sin \alpha } } =1- \frac{2sin \alpha cos \alpha }{ sin^{2} \alpha + cos^{2} \alpha } =1-2sin \alpha cos \alpha$=
$(sin \alpha -cos \alpha )^{2} = (- \frac{1}{3}) ^{2} = \frac{1}{9}$