Question

prove the identity:
1-tanx/1+tanx =1-sin 2x/cos 2x

Answer 1

\[\frac{1-tanx}{1+tanx} = \frac{1-\frac{sinx}{cosx}}{1+\frac{sinx}{cosx}} = \frac{cosx - sinx}{cosx+sinx}\]

Answer 2

now multiply by
\[\frac{cosx-sinx}{cosx-sinx}\]