LHS=(cos^2(alpha+beta)+cos^2(alpha -beta))/(2sin^2alphasin^2beta)
=((cosalphacosbeta-sinalphasinbeta)^2+(cosalpha cosbeta+sinalphasinbeta)^2)/(2sin^2alphasin^2beta)
=(2(cos^2alphacos^2beta+sin^2alphasin^2beta))/(2sin^2alphasin^2beta)
=(cos^2alphacos^2beta)/(sin^2alphasin^2beta)+(sin^2alphasin^2beta)/(sin^2alphasin^2beta)
=cot^2alphacot^2beta+1=RHS