Question 366648
Since {{{cos(x)=5/12}}}, this means that {{{sin(x)=sqrt(1-cos^2(x))=sqrt(1-(5/12)^2)=sqrt(119/144)=sqrt(119)/12}}}



Also, because {{{cos(y)=11/12}}}, this means that {{{sin(y)=sqrt(1-cos^2(y))=sqrt(1-(11/12)^2)=sqrt(23/144)=sqrt(23)/12}}}



Now use the identity {{{cos(x-y)=cos(x)cos(y)+sin(x)sin(y)}}} to get: 



{{{cos(x-y)=cos(x)cos(y)+sin(x)sin(y)=(5/12)(11/12)+(sqrt(119)/12)(sqrt(23)/12)=55/144+sqrt(2737)/144=(55+sqrt(2737))/144}}}



So {{{cos(x-y)=(55+sqrt(2737))/144}}} when {{{cos(x)=5/12}}} and {{{cos(y)=11/12}}}