(tan x + cot x)^2 -csc^2x
=tan^2x+2tanxcotx+cot^2x-csc^2x
=sin^2x/cos^2x + 2 + cos^2x/sin^2x - 1/sin^2x
=sin^2x/cos^2x + 2 +(cos^2x- 1)/sin^2x
=sin^2x/cos^2x + 2 +(-sin^2x)/sin^2x
=sin^2x/cos^2x + 2 -1
=sin^2x/cos^2x + 1
=(sin^2x+cos^2x )/cos^2x
=1/cos^2x
=sec^2x