Jika Tg x = 6 dan Sin (x – y)= 2Cos (y – x), maka Ctg y = ...

[tex]\displaystyle \sin(x-y)=2\cos(y-x)\\\sin(x-y)=2\cos(-[x-y])\\\sin(x-y)=2\cos(x-y)\\\frac{\sin(x-y)}{\cos(x-y)}=2\\\tan(x-y)=2\\\frac{\tan x-\tan y}{1+\tan x\tan y}=2\\\frac{6-\tan y}{1+6\tan y}=2\\6-\tan y=2+12\tan y\\4=13\tan y\\\tan y=\frac4{13}\\\boxed{\boxed{\cot y=\frac{13}4}}[/tex]