How do you verify (2tan(x/2)) / (1+tan^2(x/2)) = sin x2tan(x2)1+tan2(x2)=sinx?

1 Answer
Mar 9, 2018

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Explanation:

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