Question

Prove that `(tanx-cotx)/(tanx+cotx)=1-2cos^2x`?

Answer 1

We saw here http://socratic.org/questions/prove-that-tanx-cotx-tanx-cotx-1-2cos2x#174023

that `(tanx-cotx)/(tanx+cotx)=-cos2x`

but `cos2x=cos^2x-sin^2x=cos^2x-(1-cos^2x)=2cos^2x-1`

substitute the last to the result we found to get what you want.