cot(2x)=cos(2x)/sin(2x)=(1-2(sin(x))^2)/2sin(x)cos(x).
In the right-angled triangle ABC drawn on x-y axis, A is point (-12,0), B is (0,0) and C is (0,-5). Angle ABC is a right-angle and BAC=x. cos(x)=AB/AC=-12/13. BC=sqrt(AC^2-AB^2)=sqrt(13^2-12^2)=sqrt(25)=5. sin(x)=BC/AC=-5/13 (cosec(x)<0). cot(2x)=(1-2(25/169)/(2*(-5/13)(-12/13)=(169-50)/120=119/120.