How to prove these identities?

Question

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

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Answer 1 · 2016-12-08T10:54:07

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

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

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

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

$=1/(cos2theta)+tan2theta$

$=sec2theta+tan2theta=RHS$

Proved