Question

Найдите ctg (x-y) если cosx*siny=2/3
sinx*cosy=(-1/3)

Answer 1

$cosx \cdot siny - sinx \cdot cosy = sin(y - x) \\ \\ sin(y - x) = \dfrac{2}{3} + \dfrac{1}{3} = 1 \\ \\ sin(x - y) = -sin(y - x) = -1 \\ \\ cos(x - y) = \sqrt{1 - sin^2(x - y)} = \sqrt{1 - 1} = 0 \\ \\ ctg(x - y) = \dfrac{cos(x - y)}{sin(x - y)} = \dfrac{0}{-1} = 0$

Answer 2

{sinxcosy=-1/3
{cosx*siny=2/3
отнимем
sinxcosy-sinycosx=-1
sin(x-y)=-1
cos(x-y)=√1-sin²(x-y)=√(1-1)=0
ctg(x-y)=cos(x-y)/sin(x-y)=0:(-1)=0