How do you find a double angle formula for sec(2x) in terms of only csc(x) and sec(x)?

##sec2x##
##=1/cos(2x)##
##=1/(cos^2x-sin^2x)##
##=1/(cos^2xsin^2x(1/sin^2x-1/cos^2x))##
##=(1/(cos^2x)1/sin^2x)/(1/sin^2x-1/cos^2x)##
##=(sec^2xcsc^2x)/(csc^2x-sec^2x)##