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How do you verify ##(1+cos2x)/(sin2x) = cotx##?
Since
##cos2x=cos^2x-sin^2x=1-2sin^2x=2cos^2x-1##
and
##sin2x=2sinxcosx##
then:
##(1+2cos^2x-1)/(2sinxcosx)=cotxrArr##
##(2cos^2x)/(2sinxcosx)=cotxrArr##
##cosx/sinx=cotxrArr##
##cotx=cotx##.