Question

How to prove these identities?

`(1 + tantheta)/(1-tantheta) =sec 2theta + tan 2theta`

Answer 1

`LHS=(1+tantheta)/(1-tantheta)`

`=(1+tantheta)^2/((1-tantheta)(1+tantheta))`

`=(1+tan^2theta+2tantheta)/(1-tan^2theta)`

`=(1+tan^2theta)/(1-tan^2theta)+(2tantheta)/(1-tan^2theta)`

`=1/(cos2theta)+tan2theta`

`=sec2theta+tan2theta=RHS`

Proved