Cosx=1-tan^2(x/2)/1+tan^2(x/2)?

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

`Cosx=(1-((1-cosx)/sinx)^2)/(1+((1-cosx)/sinx)^2)`

`Cosx=(1-((1-2cosx+cos^2x)/sin^2x))/(1+((1-2cosx+cos^2x)/sin^2x))`

`Cosx=(sin^2x/sin^2x-((1-2cosx+cos^2x)/sin^2x))/(sin^2x/sin^2x+((1-2cosx+cos^2x)/sin^2x))`

`Cosx=((2cosx-2cos^2x)/sin^2x)/((2-2cosx)/sin^2x)`

`Cosx=(cancel(2)cosxcancel((1-cosx)))/cancel(sin^2x)*cancel(sin^2x)/(cancel2cancel((1-cosx))`

`cosx=cosx`