Perform the addition or subtraction.

Question

tanx - sec^2x/tanx

tan^2(x)/tan(x) - sec^2x/tanx =

tan^2x sec^2x / tanx

then I use the identity 1+tan^2u=sec^2u

I do not know what to do at this point.

Answer 1

from you second line
tan^2(x)/tan(x) - sec^2x/tanx
= (tan^2 x - sec^2 x)/tanx
= (tan^2 x - (1 + tan^2 x))/tanx
= -1/tanx or -cotx or -sinx/cosx