Question

How do you prove that `(1 + tan^2x)/(1 + cot^2x) = ((1 - tanx)/(1 - cotx))^2`?

Answer 1

`(1 + sin^2x/cos^2x)/(1 + cos^2x/sin^2x) = ((1 - sinx/cosx)/(1 - cosx/sinx))^2`

`((cos^2x + sin^2x)/cos^2x)/((sin^2x + cos^2x)/sin^2x) = (((cosx - sinx)/cosx)/((sinx - cosx)/sinx))^2`

`sin^2x/cos^2x = (-sinx/cosx)^2`

`sin^2x/cos^2x= sin^2x/cos^2x`

Hopefully this helps!