Question

How do you verify `cos 2x = (1-tan^2x)/(1+tan^2x)` using the double angle identity?

Answer 1

`LHS=cos2x=cos(x+x)`

`=cosx*cosx-sinx*sinx`

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

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

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

Verified