LHS : (2tan(x/2))/(1+tan^2(x/2))LHS:2tan(x2)1+tan2(x2)
=((2sin(x/2))/cos(x/2))/sec^2(x/2)=2sin(x2)cos(x2)sec2(x2)-> use the property 1+tan^2x=sec^2x1+tan2x=sec2x
=((2sin(x/2))/cos(x/2))/(1/cos ^2(x/2))=2sin(x2)cos(x2)1cos2(x2)
=(2sin(x/2))/cos(x/2) * cos ^2(x/2)/1=2sin(x2)cos(x2)⋅cos2(x2)1
=(2sin(x/2))/cancelcos(x/2) * cos ^cancel2(x/2)/1
=2sin(x/2)cos(x/2)
=sin2(x/2)->use the property sin2x=2sinxcosx
=sincancel2(x/cancel2)
=sinx
=RHS