How do you simplify sec^2x(1 + cot^2x) using fundamental identities

sec^2x (1 + cot^2x) =

1/ cos^2x (1  + cos^2x / sin^2x) =

1/ cos^2x +  1/sin^2x =

sec^2x + csc^2x

(Whether this is any more "simple" than the original expression is debatable...)

Note, oddly, that 1 + cot^x = csc^2x

So

sec^2x (csc^2x) =

sec^2x csc^2x

Thus the sum of the two functions, in this case = their products....!!!