Question

How do you prove that `cot^2x = (1+cos2x)/(1-cos2x)`?

Answer 1

`cos2x= (1-tan^2x)/(1+tan^2x)`

`=> (1+cos2x)/(1-cos2x) = (1+((1-tan^2x)/(1+tan^2x)) )/(1-((1-tan^2x)/(1+tan^2x)))`

`(1+tan^2x+1-tan^2x)/(1+tan^2x-1+tan^2x)`

`= 2/(2tan^2x)=cot^2x`