How do you verify $(Cos2x)/(1-sin2x)=(1+tanx)/(1-tanx)$ ?

Question

11990 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-12T05:07:51

$LHS=(cos2x)/(1-sin2x)$

$=(cos^2x-sin^2x)/(cos^2x+sin^2x-2sinxcosx)$

$=((cosx+sinx)(cosx-sinx))/(cosx-sinx)^2$

$=(cosx+sinx)/(cosx-sinx)$

$=(cosx/cosx+sinx/cosx)/(cosx/cosx-sinx/cosx)$

$=(1+tanx)/(1-tanx)=RHS$

How do you verify (Cos2x)/(1-sin2x)=(1+tanx)/(1-tanx)(Cos2x)/(1-sin2x)=(1+tanx)/(1-tanx)?